Authors:Lorenzo Cerboni Baiardi; Ahmad K. Naimzada Pages: 47 - 61 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Lorenzo Cerboni Baiardi, Ahmad K. Naimzada Imitation-based behaviors are considered in economics with significant contributions in reference to homogeneous populations where players are characterized by the same decisional processes (see for example [42,48]). However, the presence of imitation behaviors is detected in experimental oligopolies coexisting with rational-like rules. This motivates us to consider an heterogeneous population where best responders and imitators coexist and compete in a deterministic oligopoly framework. The model we formulate is characterized by two stationary states, specifically the Cournot–Nash equilibrium and a further production level at which best responders are inactive and imitators produce at the marked clearing price. The heterogeneities among players give to the model a nonlinear structure, influence the stability properties of the Cournot–Nash equilibrium and give rise to complex dynamic scenarios. We found that the imitators’ relative fraction have an ambiguous role in determining the stability properties of the Cournot–Nash equilibrium and, provided intermediate values of the population size, its variations may cause the occurrence of both flip and Neimark–Sacker bifurcations. Chaotic dynamics and coexistent attractors, characterized by not connected basins, may also be observed. We finally note that certain dynamic regimes, described by the model, are provided by analogous features as those characterizing experimental outcomes and several experiments can be reproduced with different parameters’ sets.

Authors:Hao Chen; Wen Lv; Tongtong Zhang Pages: 1 - 14 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Hao Chen, Tongtong Zhang, Wen Lv We present a comparison of four block preconditioning strategies for linear systems arising in the numerical discretization of time–space fractional diffusion equations. In contrast to the traditional time-marching procedure, the discretization via finite difference is considered in a fully coupled time–space framework. The resulting fully coupled discretized linear system is a summation of two Kronecker products. The four preconditioning methods are based on block diagonal, banded block triangular and Kronecker product splittings of the coefficient matrix. All preconditioning approaches use structure preserving methods to approximate blocks of matrix formed from the spatial fractional diffusion operator. Numerical experiments show the efficiency of the four block preconditioners, and in particular of the banded block triangular preconditioner that usually outperforms the other three when the order of the time fractional derivative is close to one.

Authors:Adnan Daraghmeh; Naji Qatanani; Carsten Hartmann Pages: 119 - 136 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Adnan Daraghmeh, Naji Qatanani, Carsten Hartmann In this article we study balanced model reduction of linear systems for feedback control problems. Specifically, we focus on linear quadratic regulators with collocated inputs and outputs, and we consider perturbative approximations of the dynamics in the case that the Hankel singular values corresponding to the hardly controllable and observable states go to zero. To this end, we consider different perturbative scenarios that depend on how the negligible states scale with the small Hankel singular values, and derive the corresponding limit systems as well as approximate expressions for the optimal feedback controls. Our approach that is based on a formal asymptotic expansion of an algebraic Riccati equations associated with the Pontryagin maximum principle and that is validated numerically shows that model reduction based on open-loop balancing can also give good closed-loop performance.

Authors:Fernando Tura Pages: 137 - 143 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Fernando Tura A generalized lollipop graph is formed by connecting a tree and a threshold graph with an edge. Motivated by a sequence of algorithms that compute the characteristic polynomial of some classes of graphs, we present an algorithm for computing the characteristic polynomial of generalized lollipop graph with relation to signless Laplacian matrix Q . As application, we show how to construct graphs having Q -cospectral mate.

Authors:Lili Li; Boya Zhou; Xiaoli Chen; Zhiyong Wang Pages: 144 - 152 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Lili Li, Boya Zhou, Xiaoli Chen, Zhiyong Wang This paper is concerned with numerical solutions of nonlinear time fractional reaction–diffusion equations with time delay. A linearized compact finite difference scheme is proposed to solve the equations. In terms of a new developed fractional Gronwall type inequality, convergence and stability of the proposed scheme are obtained. Numerical experiments are given to illustrate the theoretical results.

Authors:Ekin Uğurlu; Dumitru Baleanu; Kenan Taş Pages: 153 - 157 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Ekin Uğurlu, Dumitru Baleanu, Kenan Taş In this paper we construct the Weyl–Titchmarsh theory for the fractional Sturm–Liouville equation. For this purpose we used the Caputo and Riemann–Liouville fractional operators having the order is between zero and one.

Authors:Rongchang Li; Qingling Zhang Pages: 158 - 178 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Rongchang Li, Qingling Zhang This paper focuses on the problem of robust H∞ sliding mode observer (SMO) design for a class of Takagi–Sugeno (T–S) fuzzy descriptor systems with time-varying delay. A SMO is designed by taking the control input and the measured output into account. Then a novel integral-type sliding surface, which involves the SMO gain matrix, is constructed for the error system. By using an appropriate Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamic to be robustly admissible with H∞ performance and determines the SMO gain matrix. Moreover, a sliding mode control (SMC) law is synthesized such that the reachability can be ensured. Finally, simulations are presented to show the effectiveness of our results.

Authors:Francesca Bellamoli; Lucas O. Müller; Eleuterio F. Toro Pages: 190 - 213 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Francesca Bellamoli, Lucas O. Müller, Eleuterio F. Toro There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph transport in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available.

Authors:Suxia Zhang; Hongbin Guo Pages: 214 - 233 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Suxia Zhang, Hongbin Guo We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for each successive infectious stage during a long infective period. The model can describe disease progression through multiple infectious stages as in the case of HIV, hepatitis B and hepatitis C. Mathematical analysis shows that the global dynamics are completely determined by the basic reproductive number R 0 . If R 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable and the disease dies out. If R 0 > 1 , a unique endemic equilibrium is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability of endemic equilibria utilizes a Lyapunov functional. Numerical simulations are illustrated and model generalization is also discussed.

Authors:Tong Zhang; JiaoJiao Jin; Tao Jiang Pages: 234 - 266 Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Tong Zhang, JiaoJiao Jin, Tao Jiang In this paper, the decoupled Crank–Nicolson/Adams–Bashforth scheme for the Boussinesq equations is considered with nonsmooth initial data. Our numerical scheme is based on the implicit Crank–Nicolson scheme for the linear terms and the explicit Adams–Bashforth scheme for the nonlinear terms for the temporal discretization, standard Galerkin finite element method is used to the spatial discretization. In order to improve the computational efficiency, the decoupled method is introduced, as a consequence the original problem is split into two linear subproblems, and these subproblems can be solved in parallel. We verify that our numerical scheme is almost unconditionally stable for the nonsmooth initial data (u 0, θ 0) with the divergence-free condition. Furthermore, under some stability conditions, we show that the error estimates for velocity and temperature in L 2 norm is of the order O ( h 2 + Δ t 3 2 ) , in H 1 norm is of the order O ( h 2 + Δ t ) , and the error estimate for pressure in a certain norm is of the order O ( h 2 + Δ t ) . Finally, some numerical examples are provided to verify the established theoretical findings and test the performances of the developed numerical scheme.

Authors:Qiao-li Dong; Li-qun Cao; Xin Wang; Ji-zu Huang Pages: 16 - 35 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Qiao-li Dong, Li-qun Cao, Xin Wang, Ji-zu Huang This paper reports a multiscale analysis and numerical algorithms for the elastic wave equations with rapidly oscillating coefficients. We mainly focus on the first-order and the second-order multiscale asymptotic expansions for the wave equations, which is proved to enjoy an explicit convergence rate. In our method, the homogenized equations are discretized by the finite element method in space and a symplectic geometric scheme in time. The multiscale solutions are then obtained efficiently by the standard multisclae asymptotic expansion framework. Several numerical simulations are carried out to validate the predicted convergence results.

Authors:Liping Xu; Zhi Li Pages: 36 - 46 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Liping Xu, Zhi Li In this paper, we consider a class of stochastic fractional evolution equations with infinite delay and a fractional Brownian motion in a Hilbert space. By the stochastic analysis technique, we establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz condition with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory.

Authors:Jinliang Shao; Lei Shi; Mengtao Cao; Hong Xia Pages: 47 - 59 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Jinliang Shao, Lei Shi, Mengtao Cao, Hong Xia A distributed containment control problem for asynchronous discrete-time second-order multi-agent systems with switching topologies is studied in this paper, where asynchrony means that each agent only receives the state information of its neighbors at certain discrete time instants determined by its own clock that is independent of other agents. Based on a novel containment control protocol, the asynchronous system is transformed into a matrix-vector form, which implies that the asynchronous containment control problem can be converted to a convergence problem of the product of infinite time-varying nonnegative matrices whose all row sums are less than or equal to 1. Then the relations between switching communication topologies and the composite of binary relation are exploited to solve this convergence problem. Finally, we obtain a sufficient condition that all the followers can enter and keep moving in the convex hull formed by the leaders if the union of the effective communication topologies across any time intervals with some given length contains a spanning forest rooted at the leaders. Moreover, some simulation examples are presented for illustration.

Authors:Erivelton G. Nepomuceno; Heitor M. Rodrigues Junior; Samir A.M. Martins; Matjaž Perc; Mitja Slavinec Pages: 67 - 75 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Erivelton G. Nepomuceno, Heitor M. Rodrigues Junior, Samir A.M. Martins, Matjaž Perc, Mitja Slavinec Interval arithmetic applied to simulation of dynamical systems has attracted a great deal of interest in recent years. Much of this research has been carried out in the calculation of fixed points or low-period windows for nonlinear discrete maps. This study proposes a novel interval computation based on a piecewise method to calculate periodic orbits for the logistic map. Using the cobweb plot, three rounding situations have been applied to a correct outward rounding, as required by interval arithmetic. The proposed method is compared with results in the literature and with the results obtained by means of the Matlab toolbox Intlab. The comparison is accomplished for nine case studies using the logistic map. Numerical results explicitly indicate that the proposed method produces intervals that are substantially narrower than those obtained with the traditional techniques.

Authors:S. Kheybari; M.T. Darvishi Pages: 76 - 93 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): S. Kheybari, M.T. Darvishi A new semi-analytical algorithm is presented to solve general multi-point boundary value problems. This method can be applied on nth order linear, nonlinear, singular and nonsingular multi-point boundary value problems. Mathematical base of the method is presented; convergence of the method is proved. Also, the algorithm is applied to solve multi-point boundary value problems including nonlinear sixth-order, nonlinear singular second-order five-point boundary value problems, and a singularly perturbed boundary value problem. Comparison results show that the new method works more accurate than the other methods.

Authors:Guangfu Wang; Shuchao Li; Dongchao Qi; Huihui Zhang Pages: 94 - 106 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Guangfu Wang, Shuchao Li, Dongchao Qi, Huihui Zhang Given a connected graph G, the edge-Szeged index Sze (G) is defined as S z e ( G ) = ∑ e = u v ∈ E m u ( e ) m v ( e ) , where mu (e) and mv (e) are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u. In this paper, some extremal problems on the edge-Szeged index of unicyclic graphs are considered. All the n-vertex unicyclic graphs with a given diameter having the minimum edge-Szeged index are identified. Using a unified approach we identify the n-vertex unicyclic graphs with the minimum, second minimum, third minimum and fourth minimum edge-Szeged indices.

Authors:Andrei D. Polyanin; Inna K. Shingareva Pages: 107 - 137 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Andrei D. Polyanin, Inna K. Shingareva Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. Solutions of such problems have singularities whose positions are unknown a priori (for this reason, the standard numerical methods for solving problems with blow-up solutions can lead to significant errors). The first proposed method is based on the transition to an equivalent system of equations by introducing a new independent variable chosen as the first derivative, t = y x ′ , where x and y are independent and dependent variables in the original equation. The second method is based on introducing a new auxiliary nonlocal variable of the form ξ = ∫ x 0 x g ( x , y , y x ′ ) d x with the subsequent transformation to the Cauchy problem for the corresponding system of ODEs. The third method is based on adding to the original equation of a differential constraint, which is an auxiliary ODE connecting the given variables and a new variable. The proposed methods lead to problems whose solutions are represented in parametric form and do not have blowing-up singular points; therefore the transformed problems admit the application of standard fixed-step numerical methods. The efficiency of these methods is illustrated by solving a number of test problems that admit an exact analytical solution. It is shown that: (i) the methods based on nonlocal transformations of a special kind are more efficient than several other methods, namely, the method based on the hodograph transformation, the method of the arc-length transformation, and the method based on the differential transformation, and (ii) among the proposed methods, the most general method is the method based on the differential constraints. Some examples of nonclassical blow-up problems are considered, in which the right-hand side of equations has fixed singular points or zeros. Simple theoretical estimates are derived for the critical value of an independent variable bounding the domain of existence of the solution. It is shown by numerical integration that the first and the second Painlevé equations with suitable initial conditions have non-monotonic blow-up solutions. It is demonstrated that the method based on a nonlocal transformation of the general form as well as the method based on the differential constraints admit generalizations to the nth-order ODEs and systems of coupled ODEs.

Authors:Dominik Sierociuk; Michal Macias; Wiktor Malesza Pages: 138 - 147 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Dominik Sierociuk, Michal Macias, Wiktor Malesza The aim of the paper is to give a method for modeling and practical realization of iterative fractional variable-type and -order difference operator. Based on already known serial switching scheme, it was unable to obtain practical realization of such an operator. Therefore, a new parallel switching scheme is introduced. The equivalence between proposed switching scheme and variable-type operator is proved as well. Using proposed method an analog realization of fractional variable-type and -order difference operator is presented and comparison of experimental and numerical results are given.

Authors:Yi Chen; Shuai Ding; Handong Zheng; Youtao Zhang; Shanlin Yang Pages: 148 - 161 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Yi Chen, Shuai Ding, Handong Zheng, Youtao Zhang, Shanlin Yang Mobile health (mHealth) is an emerging healthcare practice that provides public health information and medical care services using mobile communication devices, such as smartphones and tablet computers. Given the service convenience and the great potential in reducing medical expense, the promotion of mHealth has become an indispensable component of healthcare reform in China. While Chinese government has shown strong support in promoting mHealth, the behaviors of different participants in mHealth have not been well studied, which prevents its fast diffusion in China. In this paper, by analyzing the current status of mHealth in China, we leverage the evolutionary game theory to build a novel model to capture the behaviors of two key participants, e.g., hospitals and patients, in mHealth. We analyze the payoff matrix between hospitals and patients such that a replicator dynamic system can be built. We validate the proposed model with detailed simulations. Our observations benefit not only the mHealth participants but also the government policy makers.

Authors:Robert Williams Pages: 162 - 175 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Robert Williams The brain encodes spatial structure through a combinatorial code of neural activity. Experiments suggest such codes correspond to convex areas of the subject’s environment. We present an intrinsic condition that implies a neural code may correspond to a collection of convex sets and give a bound on the minimal dimension underlying such a realization.

Authors:Vishnu Narayan Mishra; Ankita R. Devdhara; R.B. Gandhi Pages: 206 - 214 Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Vishnu Narayan Mishra, Ankita R. Devdhara, R.B. Gandhi In this paper, Investigation of global approximation of the generalized Szàsz–Mirakjan type operators in exponential weight spaces is discussed. The paper focuses on calculation of moments, direct results and inverse results for the saturated as well as non-saturated cases.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Yuxia Yang, Chong Lin, Bing Chen, Qing-Guo Wang This paper investigates the H ∞ reduced-order observer design problem for a class of nonlinear systems with interval time-varying delay which satisfies the quadratically inner-bounded condition and encompasses the family of Lipschitz systems. A novel reduced-order observer design methodology for nonlinear systems is proposed. By utilizing a newly extended reciprocal convexity inequality, free-weighting matrix technique, and quadratically inner-bounded condition, the less conservative existence conditions of the proposed nonlinear H ∞ observer are derived. The new sufficient conditions in terms of linear matrix inequalities (LMIs) guarantee asymptotic stability of the estimation error dynamics with a prescribed performance γ. Two numerical examples are given to illustrate the effectiveness of the proposed approach.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Alessandro Buccini, Yonggi Park, Lothar Reichel The solution of discrete ill-posed problems has been a subject of research for many years. Among the many methods described in the literature, the Bregman algorithm has attracted a great deal attention and been widely investigated. Recently, a nonstationary preconditioned version of this algorithm, referred to as the nonstationary modified linearized Bregman algorithm, was proposed. The aim of this paper is to discuss numerical aspects of this algorithm and to compare computed results with known theoretical properties. We also discuss the effect of several parameters required by the algorithm on the computed solution.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Zhehao Zhang We start with applying two methods to derive formulas of a mixture of exponential process, i.e., a renewal process whose inter-arrival time follows a mixture of exponentials. Further, stochastic order properties are discussed when comparing this process to a Poisson process with the same expectation of inter-arrival times. Based on these properties, formulas and ordering properties are given for the non-discounted compound process as well as the discounted one. Explicit formulas for the density functions are also provided for both cases. Under the discounted compound case, several new results are derived for heavy-tailed distributions. Finally, the Laguerre series approximation is proposed and tested for various common actuarial indices, e.g., VaR, CTE and stop-loss premium.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Caihong Zhang, Yonggui Kao, Binghua Kao, Tiezhu Zhang In this paper, the stability problem for delayed Markovian jump stochastic parabolic It o ^ equations (DMJSPIEs) subject to generally uncertain transition rates (GUTRs) is investigated via Lyapunov-Krasovskii functional and linear matrix inequality (LMI) method. In the model discussed, we suppose that only part of the transition rates of the jumping process are known, namely, some factors have been already available, some elements have been simply known with lower and upper bounds, and the rest of elements may have no useful information. Lastly, the applicability and effectiveness of the obtained results are illustrated through an example.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Malika Sader, Abdujelil Abdurahman, Haijun Jiang This paper studies the general decay synchronization of a class of bidirectional associative memory neural networks with time-varying delays. First, a useful lemma which generalizes the classical exponential synchronization and polynomial synchronization is introduced. Then by using this lemma, some simple sufficient criteria ensuring the general decay synchronization of considered bidirectional associative memory neural networks are obtained via designing a novel nonlinear feedback controller and using some inequality techniques. Finally, two numerical examples are provided to demonstrate the feasibility of the established theoretical results. The results of this paper are general since the classical polynomial synchronization and exponential synchronization can be seen the special cases of general decay synchronization.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Yufeng Zhang, Jianqin Mei, Xiangzhi Zhang One generalized Burgers hierarchy is derived by applying the Cole-Hopf transforation, whose dark-equation hierarchy is also generated by the dark-equation method, from which a generalized Burgers equation and a generalized Kupershmidt equation, respectively, are followed to obtain. Through Lie-group analysis method we produce similarity reductions, exact solutions of the generalized Burgers and the Kupershmidt equations. Specially, we investigate the similarity reductions of the fractional Kupershmidt equation and its exact solutions. In addition, we obtain the conservation laws of the Kupershmidt equation and its adjoint equation. Finally, we give rise to symmetries, primary branch solutions as well various recursion operators of degenerated equations from the Kupershmidt equation.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Yao Xu, Chenyin Chu, Wenxue Li In this paper, finite-time inner synchronization of coupled systems on a network with time delay and distributed delay (CSNTD) is investigated. And here, time delay and distributed delay are both taken into consideration when modelling a realistic network. Different from common feedback control, the controller we design is quantized, which is more realistic and reasonable. By using Lyapunov method and Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are derived to guarantee finite-time inner synchronization of CSNTD. It should be underlined that the method is first applied to studying the issue of finite-time inner synchronization of CSNTD and the synchronization time we obtain has a close relationship with the topological structure of the network. Moreover, to verify our theoretical results, we present an application to coupled oscillators with time delay and distributed delay, and a sufficient criterion is obtained. Ultimately, a numerical example is given to verify the validity and feasibility of theoretical results.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Yinkui Li, Ruijuan Gu For a given graph G = ( V , E ) , denote by m(G) and ω(G) the order of the largest component and the number of components of G, respectively. The scattering number of G is defined as s ( G ) = max { ω ( G − X ) − X : X ⊆ V , ω ( G − X ) > 1 } , and the rupture degree r ( G ) = max { ω ( G − X ) − X − m ( G − X ) : X ⊆ V ( G ) , ω ( G − X ) > 1 } . These two parameters are related to reliability and vulnerability of networks. In this paper, we present some new bounds on the scattering number and rupture degree of a graph G in terms of its connectivity κ(G) and genus γ(G). Furthermore, we give graphs to show these bounds are best possible.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Meng Liu, Jingyi Yu, Partha Sarathi Mandal This work is concerned with a two-species stochastic state-switching competitive population model with distributed delays and harvesting. First, necessary and sufficient criteria for the existence of a unique ergodic stationary distribution of the system are established. Then necessary and sufficient criteria for the existence of the optimal harvesting policy are given, and the explicit expression of the optimal harvesting policy is obtained. Finally, some effects of the state-switching on the persistence, extinction and optimal harvesting strategy of the system are discussed with the help of several simulations.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Niko Tratnik In this paper, we study the Steiner hyper-Wiener index of a graph, which is obtained from the standard hyper-Wiener index by replacing the classical graph distance with the Steiner distance. It is shown how this index is related to the Steiner Hosoya polynomial, which generalizes similar result for the standard hyper-Wiener index. Next, we show how the Steiner 3-hyper-Wiener index of a modular graph can be expressed by using the classical graph distances. As the main result, a method for computing this index for median graphs is developed. Our method makes computation of the Steiner 3-hyper-Wiener index much more efficient. Finally, the method is used to obtain the closed formulas for the Steiner 3-Wiener index and the Steiner 3-hyper-Wiener index of grid graphs.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Xianliang Liu, Zishen Yang, Wei Wang In this paper, we consider a variation of the classic dominating set problem - The Two Disjoint Connected Dominating Sets (DCDS) problem, which finds applications in many real domains including wireless sensor networks. In the DCDS problem, we are given a graph G = ( V , E ) and required to find a new edge set E′ with minimum cardinality such that the resulting new graph after the adding of E′ has a pair of disjoint connected dominating sets. This problem is very hard in general graphs, and we show that it is NP -hard even restricted to trees. We also present a polynomial time approximation algorithm for the DCDS problem for arbitrary trees with performance ratio 3 2 asymptotically.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Lifen Jia, Waichon Lio, Xiangfeng Yang As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of α-path, and shows that the solution of an uncertain spring vibration equation can be expressed by a family of solutions of second-order ordinary differential equations. This paper also proves that the inverse uncertainty distribution of solution of uncertain spring vibration equation is just the α-path of uncertain spring vibration equation, and a numerical algorithm is designed. Moreover, a formula to calculate the expected value of solution of uncertain spring vibration equation is derived. Finally, several numerical examples are provided to illustrate the efficiency of the numerical method.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Ying Mao, Liqing Wang, Yang Liu, Jianquan Lu, Zhen Wang This paper investigates the dynamics of evolutionary networked games with different length information via semi-tensor product (STP) method. First, a networked game with different length information is modeled in the form of probabilistic Boolean networks (PBNs) with time delays. Second, based on the utility function of each player, a necessary condition for the existence of a pure Nash equilibrium is obtained. Then a state feedback control is applied to stabilize the considered system. Finally, an example is presented to substantiate the effectiveness of the theoretical results.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Hanna Okrasińska-Płociniczak, Łukasz Płociniczak In this work we prove that a family of explicit numerical methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity. In that case the kernel is not of Lipschitz type, therefore the classical analysis cannot be utilized. We indicate several difficulties that arise in the proofs and show how they can be remedied. The tools that we use consist of variations on discreet Gronwall’s lemmas and comparison theorems. Additionally, we give an upper bound on the convergence order. We conclude the paper with a construction of a convergent method and apply it for solving some examples.

Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): V. Kostić, D. Gardašević Since nonlinear eigenvalue problems appear in many applications, the research on their proper treatment has drawn a lot of attention lately. Therefore, there is a need to develop computationally inexpensive ways to localize eigenvalues of nonlinear matrix-valued functions in the complex plane, especially eigenvalues of quadratic matrix polynomials. Recently, few variants of the Geršgorin localization set for more general eigenvalue problems, matrix pencils and nonlinear ones, were developed and investigated. Here, we introduce a more general approach to Geršgorin-type sets for nonlinear case using diagonal dominance, prove some properties of such sets and show how they perform on several problems in engineering.

Authors:Olha Ivanyshyn; Yaman Gazi Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Olha Ivanyshyn Yaman, Gazi Özdemir We propose two methods based on boundary integral equations for the numerical solution of the planar exterior Robin boundary value problem for the Laplacian in a multiply connected domain. The methods do not require any a-priori information on the logarithmic capacity. Investigating the properties of the integral operators and employing the Riesz theory we prove that the obtained boundary integral equations for both methods are uniquely solvable. The feasibility of the numerical methods is illustrated by examples obtained via solving the integral equations by the Nyström method based on weighted trigonometric quadratures on an equidistant mesh.

Authors:Shuli Weigen; Yan Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Shuli Li, Weigen Yan The Cairo pentagonal lattice is the dual lattice of the (32.4.3.4) lattice. In this work, we obtain explicit expression of the number of spanning trees of the Cairo pentagonal lattice with toroidal boundary condition, particularly, there is a constant difference (not one) of the number of spanning trees between the (32.4.3.4) lattice and the Cairo pentagonal lattice with toroidal boundary condition. We also obtain the asymptotic growth constant and the dimer entropy of the Cairo pentagonal lattice with toroidal boundary condition.

Authors:Taras Agryzkov; Leandro Tortosa Jose Vicent Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Taras Agryzkov, Leandro Tortosa, Jose F. Vicent Diversity is an important measure that according to the context, can describe different concepts of general interest: competition, evolutionary process, immigration, emigration and production among others. It has been extensively studied in different areas, as ecology, political science, economy, sociology and others. The quality of spatial context of the city can be gauged through this measure. The spatial context with its corresponding dataset can be modelled using spatial networks. Consequently, this allows us to study the diversity of data present in this specific type of networks. In this paper we propose an algorithm to measure diversity in spatial networks based on the topology and the data associated to the network. In the experiments developed with networks of different sizes, it is observed that the proposed index is independent of the size of the network, but depends on its topology.

Authors:Liuliu Xie; Xiaotao Huang Lihe Wang Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Liuliu Xie, Xiaotao Huang, Lihe Wang The aim of this paper is to investigate a class of fractional p-Laplacian equations. We obtain existence and symmetry results for solutions in the fractional Sobolev space W s,p (Rn ) by rearrangement of its corresponding constrained minimization. Our results are in accordance with those for the classical p-Laplacian equations and fractional Schrödinger equations.

Authors:Kanailal Mahato Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Kanailal Mahato In this article, we discussed some fruitful estimates for the composition of Hankel wavelet transform associated with fractional Hankel transform on the Sobolev type space. Parseval’s identity is proposed for composition of Hankel wavelet transform. Plancherel’s formula is obtained. Also boundedness results of composition of Hankel wavelet transform is given on certain function spaces.

Authors:Schieweck Skrzypacz; Tobiska Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): F. Schieweck, P. Skrzypacz, L. Tobiska We construct L 2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L 2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.

Authors:Deqiang Zeng; Ruimei Zhang Xinzhi Liu Shouming Zhong Kaibo Shi Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Deqiang Zeng, Ruimei Zhang, Xinzhi Liu, Shouming Zhong, Kaibo Shi This paper is concerned with the exponential synchronization of directed complex dynamical networks (CDNs) with sampled-data communications (SDCs) via pinning stochastic sampled-data control. Different from traditional directed CDNs with determined sampling intervals, multiple stochastic varying sampling intervals with given probabilities are considered in this paper. Compared with some existing control schemes, our control method is more practical because the random sampling intervals always happen in some practical situation. In addition, a Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can fully capture the information on stochastic sampling intervals, stochastic input delays, and nonlinear functions. Based on the LKF and Wirtinger’s inequality, less conservative synchronization criteria are obtained. Finally, numerical examples are given to illustrate the effectiveness and superiorities of the proposed results.

Authors:Xuli Han Abstract: Publication date: 15 November 2018 Source:Applied Mathematics and Computation, Volume 337 Author(s): Xuli Han A united form of the classical Hermite interpolation and shape-preserving interpolation is presented in this paper. The presented interpolation method provides higher order continuous shape-preserving interpolation splines. The given interpolants are explicit piecewise rational expressions without solving a linear or nonlinear system of consistency equations. By setting parameter values, the interpolation curve can be generated by choosing the classical piecewise Hermite interpolation polynomials or the presented piecewise rational expressions. For monotonicity-preserving and convexity-preserving interpolation, the appropriate values of a parameter are given on each subinterval. Numerical examples indicate that the given method produces visually pleasing curves.

Authors:Pedro Lima; Azzeddine Bellour Mikhail Bulatov Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Pedro M. Lima, Azzeddine Bellour, Mikhail V. Bulatov We consider the numerical solution of a singular boundary value problem on the half line for a second order nonlinear ordinary differential equation. Due to the fact that the nonlinear differential equation has a singularity at the origin and the boundary value problem is posed on an unbounded domain, the proposed approaches are complex and require a considerable computational effort. In the present paper, we describe an alternative approach, based on the reduction of the original problem to an integro-differential equation. Though the problem is posed on the half-line, we just need to approximate the solution on a finite interval. By analyzing the behavior of the numerical approximation on this interval, we identify the solution that satisfies the prescribed boundary condition. Although the numerical algorithm is much simpler than the ones proposed before, it provides accurate approximations. We illustrate the proposed methods with some numerical examples.

Authors:Huifang Zhou; Zhiqiang Sheng Guangwei Yuan Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Huifang Zhou, Zhiqiang Sheng, Guangwei Yuan In this paper we present a nonlinear positivity preserving finite volume scheme for the Nagumo-type equations with anisotropic tensor diffusion coefficient. For the diffusion term, we use the positivity preserving finite volume scheme. For the time direction, we use the backward Euler approximation. We deal with nonlinear reaction term implicitly and decompose nonlinear reaction coefficient into two nonnegative functions. Thus we get a system of nonlinear algebraic equations. The advantages of our scheme are that it can be applied to distorted meshes and has no severe constraint on the time step. The numerical results verify the theoretical result.

Authors:Mine Aylin; Bayrak Ali Demir Abstract: Publication date: 1 November 2018 Source:Applied Mathematics and Computation, Volume 336 Author(s): Mine Aylin Bayrak, Ali Demir In this paper, the approximate analytic solution of any order space-time fractional differential equations is constructed by means of semi-analytical method, named as residual power series method (RPSM). The first step is to reduce space-time fractional differential equation to either a space fractional differential equations or a time fractional differential equations before applying RSPM. The main step is to obtain fractional power series solutions by RSPM. At the final step, it is shown that RPSM is very efficacious, plain and powerful for obtaining the solution of any-order space-time fractional differential equations in the form of fractional power series by illustrative examples.