Abstract: Publication date: 1 November 2019Source: Applied Mathematics and Computation, Volume 360Author(s): Huizi Yang, Zhanwen Yang, Shufang Ma In this paper, we theoretically and numerically deal with nonlinear Volterra integro-differential equations with Itô integral under a one-sided Lipschitz condition and polynomially growth conditions. It is proved that both the exact solutions and vector fields are bounded and satisfy a Hölder condition in the pth moment sense. Analogously, the boundedness and Hölder condition in the pth moment sense are preserved by the semi-implicit Euler method for sufficiently small step-size. Moreover, by the local truncated errors, we prove the strong convergence order 1. Finally, numerical simulations on stochastic control models and stochastic Ginzburg–Landau equation illustrate our results.

Abstract: Publication date: 1 November 2019Source: Applied Mathematics and Computation, Volume 360Author(s): Ali Başhan The aim of the manuscript is to investigate numerical solutions of the system of coupled Korteweg-de Vries equation. For this approximation, we have used finite difference method for time integration and differential quadrature method depending on modified cubic B-splines for space integration. To display the accuracy of the present mixed method three famous test problems namely single soliton, interaction of two solitons and birth of solitons are solved and the error norms L2 and L∞ are computed and compared with earlier works. Comparison of error norms show that present mixed method obtained superior results than earlier works by using same parameters and less number of nodal points. At the same time, two lowest invariants and amplitude values of solitons during the simulations are calculated and reported. In addition those, relative changes of invariants are computed and tabulated. Properties of solitons observed clearly at the all of the test problems and figures of the all of the simulations are given.

Abstract: Publication date: 1 November 2019Source: Applied Mathematics and Computation, Volume 360Author(s): Feng Li, Shuai Song, Jianrong Zhao, Shengyuan Xu, Zhengqiang Zhang This paper pays attention to the synchronization control issue for Markov jump neural networks with partial information on system modes (or called Markov states), which leads to the case that the system modes cannot be directly accessed. An hidden Markov model (HMM)-based detector with partially known detection probabilities is employed to detect the system modes. With the help of the HMM and an activation function dividing method, a less conservative controller design technique is established. The designed HMM-based controller can be converted to mode-independent/-dependent one by suitably adjusting some design parameters. Finally, the availability of the established HMM-based controller design technique is verified by an illustrative example.

Abstract: Publication date: 1 November 2019Source: Applied Mathematics and Computation, Volume 360Author(s): Bin Lin In this study, the parametric cubic spline scheme is implemented to find the approximate solution of the coupled nonlinear Schrödinger equations. This scheme is based on the Crank–Nicolson method in time and parametric cubic spline functions in space. The error analysis and stability of the scheme are investigated and the numerical results show that we can get different precision schemes by choosing suitably parameter values and this scheme is unconditionally stable. Two problems are solved to illustrate the efficiency of the methods as well as to compare with other methods.

Abstract: Publication date: Available online 22 May 2019Source: Applied Mathematics and ComputationAuthor(s): Rawlilson O. Araújo, Sheyla S. Marinho, Julio S. Prates Filho The Bresse system is a recognized mathematical model for vibrations of a circular arched beam that contains the class of Timoshenko beams when the arch’s curvature is zero. It turns out that the majority of mathematical analysis to Bresse systems are concerned with the asymptotic stability of linear homogeneous problems. Under this scenario, we consider a nonlinear Bresse system modeling arched beams with memory effects, in a nonlinear elastic foundation. Then we establish uniform decay rates of the energy under time-dependent external forces.

Abstract: Publication date: 1 November 2019Source: Applied Mathematics and Computation, Volume 360Author(s): Wenhui Liu, Junwei Lu, Shengyuan Xu, Yongmin Li, Zhengqiang Zhang In modern control theory, it is more applicable for digital computers using a sampled-data controller than a continuous-time controller. Meanwhile, input saturation and disturbance inevitably exist in control systems. Thus, how to propose an applicable sampled-data controller for nonlinear systems considering input saturation together with external disturbances is essential for applications. To deal with this control problem, a novel auxiliary control signal is designed in this paper. Then, by using Lyapunov method, the control design process is simplified compared with the traditional backstepping technique, and only one Lyapunov function is needed. In addition, the state and disturbance observers are proposed with the new auxiliary control signal to track the unavailable states and external disturbances. Finally, we propose a novel controller reflecting the sampled-data output-feedback for the nonlinear systems to ensure the system stability. The effectiveness of proposed control method in this paper is confirmed through two sets of numerical simulation results.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Carlos Alves Moreira, Eric Allison Philot, Angélica Nakagawa Lima, Ana Ligia Scott The phenomenon of protein aggregation has been associated with several neurodegenerative diseases, such as Parkinson's and Alzheimer's. Computational tools have been used to predict regions prone to aggregate in proteins with relative success. We have developed a tool called MAGRE for such predictions, based on the machine learning and sliding window techniques. We have applied the Support Vector Machine algorithm to generate classification models. In order to accomplish classification training, we adopted information of primary structure - protein sequence - from the Amyloid Data Bank. We have implemented two predictor categories according to protein structural information: General and Folding Class. We have selected the best performances of the sliding windows method and considered the folding class in order to develop the predictor. We conducted testing with randomly selected protein sequences from the PDB data bank - MAGRE's performance was compared with two predictors from literature: Aggrescan and Zyggregator, being considered satisfactory.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Huanbin Xue, Xiaohui Xu, Jiye Zhang, Xiaopeng Yang A class of switched neural networks (SNNs) in the presence of parameter uncertainties, impulsive effects, and both variable and continuously distributed delays are investigated. Firstly, the existence and uniqueness conditions of equilibrium point of each subsystem are proposed, which implies that the addressed SNNs has a unique equilibrium point. Secondly, we derive several sufficient conditions for robust exponential stability under average dwell time (ADT) switching and arbitrary switching, respectively. These conditions are formulated in terms of algebraic inequalities and M-matrices and are derived by employing inequality technique incorporated with the idea of vector Lyapunov function. Lastly, the less conservativeness and effectiveness of the obtained results over some existing literature are verified by simulation examples.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Li-Ying Hao, Ying Yu, Hui Li This paper designs the robust fault tolerant controller for unmanned marine vehicle (UMV) systems with thruster faults and external disturbances via sliding mode output feedback. A comprehensive and unified fault model including thruster partial, complete and stuck faults is built for the first time. Based on input matrix full-rank decomposition technique and H∞ technique, a sufficient condition of sliding mode in the form of linear matrix inequality (LMI) is given. Then taking advantage of adaptive mechanism, a nonlinear discontinuous control term and an output feedback controller are aimed to reduce the oscillation amplitudes of the yaw velocity error and the yaw angle. Compared with the existing methods, the general faults including time-varying stuck fault can be dealt with. Eventually, the comparative simulation results have demonstrated the effectiveness and feasibility of the presented strategy in this paper.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Zhaoying Wei, Guangsheng Wei In this paper we employ the Euclidean division for polynomials to recover uniquely a Jacobi matrix in terms of the mixed spectral data consisting of its partial entries and the information given on its full spectrum together with a subset of eigenvalues of its truncated matrix obtained by deleting the last row and last column, or its rank-one modification matrix modified by adding a constant to the last element. A necessary and sufficient condition is provided for the existence of the inverse problem. A numerical algorithm and a numerical example are given.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Yuanyuan Chen, Dan Li, Zhiwen Wang, Jixiang Meng The kth power of a graph G, denoted by Gk, is a graph with the same set of vertices as G such that two vertices are adjacent in Gk if and only if their distance in G is at most k. In this paper, we give upper and lower bounds on the Aα-spectral radius of G2. Furthermore, the first three largest Aα-spectral radius of the second power of trees are determined.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Haifeng Ma, Predrag S. Stanimirović Several characterizations and representations for the core-EP inverse are presented and investigated. To that goal, several explicit bordering technique for characterizing and defining the core-EP inverse are analyzed. Also the matrix splitting method and the iterative successive matrix squaring algorithm for computing the core-EP inverse are investigated. The perturbation bounds related with the core-EP inverse are also estimated.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Chein-Shan Liu, Leiting Dong In the paper, nth-order differential of a noisy signal is recast as an nth-order ordinary differential equation with an unknown right-hand side, which is an inverse problem to recover the forcing term. We derive weak-form methods to solve the inverse problem, with sinusoidal functions as test functions. By exploring the orthogonality of sinusoidal functions, the expansion coefficients in the trial functions of weak-form numerical differentiators can be determined analytically. Several examples verify the efficiency, accuracy and robustness of the weak-form numerical differentiators for computing the higher-order differentials of noisy data. Moreover, the applications of the weak-form numerical differentiators are also demonstrated, to recover the external forces of nonlinear dynamical systems with single or multiple degrees of freedoms, which are evaluated under the pollution of large noise on the measured data of displacements.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Jiarong Li, Haijun Jiang, Zhiyong Yu, Cheng Hu In this paper, an I2S2R rumor spreading model in complex networks is established and analyzed. Firstly, the threshold value is acquired to identify the existence and stability of rumor-free equilibria state and rumor equilibria state by using the next generation matrix method. Secondly, based on Routh–Hurwitz judgment, Lyapunov stability theory and LaSalle’s invariance principle, the local and global stability of rumor-free/rumor equilibrium points are discussed. Thirdly, the sensitivity analysis about the threshold value is given to analyze the impact of model parameters on rumor propagation. Finally, some numerical simulations are presented to illustrate the validity and feasibility of corresponding results.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Xiaoyun Sun, Pei Dang In this paper, we propose a novel method of computing Hilbert transform based on the mechanical quadrature method. Experiments show that the method outperforms the library function ‘hilbert’ in Matlab when the values of functions being handled are very large or approach to infinity, that is a problem we have to deal with when we compute, for instance, outer functions. As an application, we use the method to obtain the unwinding series of signals, which is a positive frequency decomposition of signals and is dependent of extraction of outer functions involving computation of Hilbert transform. The experimental results show better stability. Then, we give the transient time frequency distribution of the unwinding series of signals. Finally, experiments of noisy signals are given, and the results show that the introduced method can well resist some disturbance.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Kun Zhang, Huaguang Zhang, Yunfei Mu, Shaoxin Sun In this paper, a novel fuzzy integral reinforcement learning (RL) based tracking control algorithm is first proposed for partially unknown fuzzy systems. Firstly, by using the precompensation and augmentation techniques, a new augmented fuzzy tracking system is constructed by combining the fuzzy logic model and desired reference trajectory, where the solution of actual working feedback control policy is converted into a virtual optimal control problem. Secondly, to overcome the requirements of exact original system information, the integral RL technique is utilized to learn the fuzzy control solution, which relaxes the repeatedly transmissions of system matrices during the solving process. Thirdly, compared with the existing standard solution, some crucial and strict aforementioned assumptions are removed and the system can be partially unknown by using the designed algorithm. Besides, under the novel fuzzy control policy, the tracking objective is achieved and the stability is guaranteed by Lyapunov theory. Finally, the developed integral RL tracking control algorithm for partially unknown systems is applied in a mechanical system and the simulation results demonstrate the effectiveness of the proposed new method.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Jinhuan Wang, Yuling Xu, Yong Xu, Dedong Yang This paper investigates the time-varying formation problem for high-order multi-agent systems subject to external disturbances. The interaction topology among agents is assumed to be directed and has a directed spanning tree. A novel event-triggered integral sliding mode control strategy is proposed. It can be proved that, with the designed control law and the event-triggered condition, the desired time-varying formation will be reached. Moreover, the Zeno behavior of triggering time sequences can be avoided. Finally, a simulation example is presented to illustrate the effectiveness of the theoretical results.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Xiaohong Wang, Haibo Du, Shihua Li, Xingpeng Zhou This paper stabilizes a class of nonlinear systems with lower-triangular structure and different time delays at exponential convergence rate via output feedback domination method. An explicit construction for the output feedback stabilizer guaranteeing the globally exponential stabilization of the system is proposed, in which a scaling gain is introduced and can be designed to dominate the nonlinearities. We then analyze the exponential stability of the system via constructing a Lyapunov functional, and result in some constraints subject to the scaling gain and time-delays. Note that it is the first time to analyze the effects from time delays on the stability of lower-triangular systems. Two simulation results are provided to support the theoretical developments.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Xin Wang, Housheng Su This paper studies the consensus problem of hybrid multi-agent systems, where the multiple discrete-time and continuous-time dynamic individuals constitute a hybrid multi-agent group. Firstly, a hybrid event-triggered method is proposed. Under this method, the hybrid consensus can be achieved asymptotically. Besides, the Zeno-behavior of the hybrid multi-agent system will not make an appearance due to the special design of the hybrid event-triggered conditions. Then, a self-triggered algorithm is further proposed to avoid the continuous monitoring of event-triggered conditions. Finally, several simulation examples are presented which are comparative and show the effectiveness of the two method. Moreover, the impact of the parameters in the main results is analyzed.

Abstract: Publication date: Available online 17 May 2019Source: Applied Mathematics and ComputationAuthor(s): Chao Wu, Yunqing Huang, Jinyun Yuan Superconvergence of the second order cubic edge elements approximation is investigated on uniform and nonuniform mesh. Superconvergence of one order higher is established at the second order Gauss points for both the finite element solution and the curl of this solution. Numerical examples are presented to support our theoretical analysis.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Tian Zhang, Huabin Chen This paper considers the problems on the existence and uniqueness, the pth(p ≥ 1)-moment and the almost sure stability with a general decay for the global solution of stochastic delay differential equations with Markovian switching, when the drift term and the diffusion term satisfy the locally Lipschitz condition and the monotonicity condition. By using the Lyapunov function approach, the Barbalat Lemma and the nonnegative semi-martingale convergence theorem, some sufficient conditions are proposed to guarantee the existence and uniqueness as well as the stability with a general decay for the global solution of such equations. It is mentioned that, in this paper, the time-varying delay is a bounded measurable function. The derived stability results are more general, which not only include the exponential stability but also the polynomial stability as well as the logarithmic one. At last, two examples are given to show the effectiveness of the theoretical results obtained.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Seyed Mehdi Abedi Pahnehkolaei, Alireza Alfi, J.A. Tenreiro Machado This paper studies the stability of fractional order (FO) continuous-time quaternion-valued Leaky Integrator Echo State Neural Networks (NN). The delay independent robust stability of NN with QUAD vector field activation functions under time varying delays is derived. The analysis follows the FO Lyapunov theorem while decomposing the NN into four real-valued systems. The existence and uniqueness of the equilibrium point are also verified by means of a contraction map on the decomposed NN. The new approach is tested in the stability analysis of the FO quaternion-valued Echo State NN whitout time delays, complex-valued Echo State and quaternion-/complex-valued Hopfield NN with/without time delays. Two numerical examples demonstrate the feasibility of the proposed method.

Abstract: Publication date: Available online 14 May 2019Source: Applied Mathematics and ComputationAuthor(s): Peican Zhu, Xinyu Wang, Shudong Li, Yangming Guo, Zhen Wang Numerous efforts have been devoted to investigating the network activities and dynamics of isolated networks. Nevertheless, in practice, most complex networks might be interconnected with each other (due to the existence of common components) and exhibit layered properties while the connections on different layers represent various relationships. These types of networks are characterized as multiplex networks. A two-layered multiplex network model (usually composed of a virtual layer sustaining unaware-aware-unaware (UAU) dynamics and a physical one supporting susceptible-infected-recovered-dead (SIRD) process) is presented to investigate the spreading property of fatal epidemics in this manuscript. Due to the incorporation of the virtual layer, the recovered and dead individuals seem to play different roles in affecting the epidemic spreading process. In details, the corresponding nodes on the virtual layer for the recovered individuals are capable of transmitting information to other individuals, while the corresponding nodes for the dead individuals (which are to be eliminated) on the virtual layer should be removed as well. With the coupled UAU-SIRD model, the relationships between the focused variables and parameters of the epidemic are studied thoroughly. As indicated by the results, the range of affected individuals will be reduced by a large amount with the incorporation of virtual layers. Furthermore, the effects of recovery time on the epidemic spreading process are also investigated aiming to consider various physical conditions. Theoretical analyses are also derived for scenarios with and without required time periods for recovery which validates the reducing effects of incorporating virtual layers on the epidemic spreading process.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Dani Suandi, Karunia Putra Wijaya, Mochamad Apri, Kuntjoro Adji Sidarto, Din Syafruddin, Thomas Götz, Edy Soewono Vector control is regarded an efficient approach for preventing and reducing the spread of malaria. For several decades, insecticides have been used to suppress the population of Anopheles mosquitoes throughout the globe. It turns out that continual usage of a single compounded insecticide has massively contributed to the rise of resistant mosquitoes. Information on the evolution of insecticide resistance is considered an essential aspect in the control of Anopheles mosquitoes. In this study, a mathematical model to describe the dynamics of Anopheles mosquitoes is constructed, highlighting genetic classification based on their resistance status with respect to insecticides. Focusing on a one-locus case related to a specific insecticide class, the model is constructed according to a scenario in which the intermediate form of resistance called heterozygous resistance can be generated from random matings between susceptible and resistant mosquitoes, therefore carrying both genes. The model is governed by a three-dimensional system of differential equations that describes the interaction between homozygous wild, heterozygous, and resistant subpopulations, with three corresponding fitness levels related to their intrinsic growth rates. Criteria for the existence and stability of all existing equilibria are obtained. It is generally concluded from the model that the fitness levels heavily determine to which steady state the model solution converges. Numerical simulations indicate that long-term implementation of high doses of insecticide can increase the proportion of resistant mosquitoes significantly. Accordingly, understanding the fitness levels is very important for selecting proper intervention strategies as well as for predicting the long-term effects of the implementation of certain insecticides.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Ticao Jiao, Ju H. Park, Guangdeng Zong, Jian Liu, Yu Chen This paper is focused on the stability problem of a class of stochastic switched genetic regulatory networks, where the stable property of every subsystem is not imposed. By employing the stabilization effects of switching behaviors and stochastic differential equation theory, a sufficient condition for globally asymptotic stability in mean is derived. Furthermore, inspired by the idea of switching interval segmentation, an easily verifiable criterion is established by means of multiple discretized Lyapunov functions. Then, we extend the attained results to the case with time delays via the multiple discretized Lyapunov-Krasovskii functionals approach. Finally, the results obtained in the paper are illustrated by a numerical example.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Syed Omar Shah, Akbar Zada In this paper, we study the existence and uniqueness of solution and stability results of mixed integral dynamic system with instantaneous and noninstantaneous impulses on time scales, by using the fixed point method. The main tools to establish our results are the Grönwall’s inequality on time scales, Picard operator and abstract Grönwall lemma. Some assumptions are made to overcome the hurdles in achieving our results. At the end, an example is given that shows the validity of our main results.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Yan-Ting Xie, Shou-Jun Xu Let Γ be a simple connected graph with vertex set V(Γ). The eccentric distance sum (EDS for short) of Γ is defined as ξd(Γ)=∑v∈V(Γ)εΓ(v)DΓ(v), where ɛΓ(v) is the eccentricity of a vertex v and DΓ(v) is the sum of all distances from v to other vertices. In the paper Li and Wu [11], the strict upper bound on ξd(Γ) among the k-connected graphs Γ with an integer k even were given, and proposed an open question: the corresponding problem on k-connected graphs with k odd. In this paper, first, we divide cubic transitive graphs into two cases: super-connectedness and non-super-connectedness, and characterized non-super-connected cubic transitive graphs, filling the gaps in this field. Then, by using the characterization, we show the upper bound on EDS among (3-connected) cubic transitive graphs of order n and characterize the extremal graphs: the ladders when n≡0(mod4) and the ladders or the Möbius ladders when n≡2(mod4). Finally, we conclude the paper with conjectures about the upper bound on EDS of k-connected graphs with odd integer k ≥ 3.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Spiros D. Dafnis, Frosso S. Makri, Andreas N. Philippou In the present paper we introduce a modified consecutive system, which generalizes consecutive systems extensively studied in the literature, and we obtain its reliability when its components are functioning independently with probabilities not necessarily equal. The results are illustrated by numerical examples using MATLAB and potential applications are discussed.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Xia Wang, Mingwang Shen, Yanni Xiao, Libin Rong Zika virus is a mosquito-borne virus and can spread to humans via bites by infected vectors or through sexual contact with infectious humans. Various protective and control measures such as the use of insecticide-treated nets, condoms, indoor residual spraying and medical treatment of infected humans may mitigate the infection. In this paper, we formulate and analyze a mathematical model that incorporates these comprehensive interventions to study the impact of mosquito-to-human and sexual transmission on the disease dynamics. We obtain the basic reproduction number, study when the disease dies out, and investigate the sensitivity of the basic reproduction number on each control. Numerical results suggest that vector transmission contributes more to the basic reproduction number than sexual transmission. We also formulate the optimal control problem and obtain the necessary conditions that minimize the population of infected individuals and the associated costs. Using the cost effectiveness analysis, we show that a combination of condom use and medical treatment of infected people provides the most cost-effective strategy to control the disease.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Weijun Zeng, Hongfeng Ai, Man Zhao This paper addresses how players’ asymmetrical expectations of future interaction affect their cooperation in the two-player iterated prisoner's dilemma (IPD) game. A player’ expectation of future interaction reflects his/her willingness to continue the interaction with his/her opponent. With the application of a co-evolutionary learning model with a niching technique that is used to search optimal strategies for players, simulation experiments are conducted to present the cooperative or uncooperative outcomes between the players with distinct expectations. Results indicate that, if one player has higher expectation of future interaction than the other, the former may be exploited by the latter. Such exploitation is mainly due to the former player's higher tendency toward mutual cooperation, which triggers the latter player's unilateral defection. Considering that real-world games always involve uncertainty or external disturbance, the games with uncertain payoffs or noise are also performed. Results indicate that the exploitation also exists in the game with uncertain payoffs. However, it may be absent in the presence of high levels of noise. The reason is that the cooperative tendency of the high-expectation player declines with the increasing level of noise. As a result, the two players are engaged in only low levels of cooperation in the IPD game. Nevertheless, when asymmetrical noise is taken into account, it is the player disturbed with higher levels of noise that is exploited by the other. In other words, the player whose strategy is interfered with higher levels of noise is more afraid of endless mutual defection caused by noise, which makes he/she cooperate more than his/her opponent, even though he/she may have a lower expectation on their future interaction.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Xiufang Wang, Haiyan Yu, Gang Li, Jinmei Gao In this research, by means of a discontinuity indicator to detect troubled cells, we propose hybrid finite volume weighted essentially non-oscillatory schemes in combination with linear central schemes for hyperbolic conservation laws. In smooth regions, we apply the simple linear central schemes to save CPU time. While in discontinuous regions, we adopt WENO schemes to maintain the essentially non-oscillatory property near discontinuities. Extensive numerical examples strongly suggest that the proposed hybrid schemes can save computational cost considerably in comparison with the same order pure WENO schemes and keep steep discontinuity transition at the same time.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Yu Yang, Ai-wan Fan, Hua Wang, Hailian Lv, Xiao-Dong Zhang In graph theory and its applications, trees, BC-trees, subtrees and BC-subtrees have been extensively studied. We introduce a generalization of the BC-tree, called the multi-granular α-tree, which is a tree (of order at least α+1) where any two leaves are at a distance that is a multiple of α. We study the number of α-subtrees, through α-subtree generating functions, for generalized Bethe trees, Bethe trees and dendrimers (hyper-branched structures in molecular topology). Our results can also be used to examine the asymptotic behavior of the average order of α-subtrees in dendrimers.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Bijo S. Anand, Ullas Chandran S. V., Manoj Changat, Sandi Klavžar, Elias John Thomas A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number gp(G) of G. It is proved that S⊆V(G) is in general position if and only if the components of G[S] are complete subgraphs, the vertices of which form an in-transitive, distance-constant partition of S. If diam(G)=2, then gp(G) is the maximum of ω(G) and the maximum order of an induced complete multipartite subgraph of the complement of G. As a consequence, gp(G) of a cograph G can be determined in polynomial time. If G is bipartite, then gp(G) ≤ α(G) with equality if diam(G) ∈ {2, 3}. A formula for the general position number of the complement of an arbitrary bipartite graph is deduced and simplified for the complements of trees, of grids, and of hypercubes.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Yingnan Pan, Guang-Hong Yang This paper investigates the event-based reduced-order fuzzy filtering problem for nonlinear networked control systems with network-induced time-varying delays. A novel fuzzy filter design approach is proposed to analyze the fuzzy systems under a reduced-order scheme. The problem of mismatched membership functions is presented in the fuzzy filtering to simplify implementation complexity and increase design flexibility of the designed reduced-order filter. In addition, the integrands of the Lyapunov–Krasovskii functional are dependent of membership functions and the existence conditions of the fuzzy filtering are given by utilizing a linearization approach. Compared with the existing reduced-order filter design approaches, the time-derivatives of membership functions are considered in the analysis process for reducing the conservativeness of obtaining the maximum delay bounds. Finally, a simulation result is given to show the effectiveness and advantages of the analysis scheme.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Nezar M. Alyazidi, Magdi S. Mahmoud This paper focuses on the behavior of a linear quadratic Gaussian (LQG) controller for discrete-time systems utilizing industrial communication protocols. A new design of LQG problem is investigated for constrained networked control systems by using a new class of a quadratic cost function with a communication cost. This paper is considered two industrial communication protocols namely: the transportation control protocol (TCP), in which the sender should receive an acknowledgment regarding the delivery of the sending packets and the user datagram protocol (UDP) where the acknowledgment signal is absence. In the latter one, the driver (actuation) does not afford acknowledgment to inform the controller/estimator regarding the reception of the action packets. In such setting, the UDP-like protocol can react nonlinearly, where the absence of the acknowledgment creates a nonlinear optimization control law. In this sense, a LQG with standard Kalman filtering is failed because the separation principle can not reached. Under this setting, a suboptimal methodology can be successfully implemented to compensate the absence of communication and acknowledgment packets. The prescribed performance of networked system is sustained in the presence of communication constraints. The probabilities of the data signal dropouts are expressed in terms of random Bernoulli processes. Then, simulation results are provided to demonstrate the validity of the proposed schemes and to compare them with others from literature.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Alexander Pleshkevich, Dmitriy Vishnevskiy, Vadim Lisitsa In this paper, we present a pseudo-spectral method to solve the one-way wave equation. The approach is a generalization of the phase-shift plus interpolation technique which is used in geophysical applications. We construct a solution at each depth layer as a linear combination of the solutions corresponding to the models with uniform reference velocities. We suggest using three-term relations to interpolate the solution with the sixth order of accuracy to the deviation from the vertical direction. Standard phase-shift plus interpolation technique uses two-terms relation interpolating the solution with the fourth order. As a result, the numerical error of the suggested approach is one half of that of the PSPI methods for a fixed set of reference velocities for a wide range of spatial discretizations and directions of wave propagation. Consequently, to compute a solution with prescribed accuracy, the presented approach allows using 20% fewer reference velocities than the PSPI. Additionally provided experiments illustrate the efficiency of the suggested approach for simulation of down-going wave propagation in complex geological media, making the algorithm a promising one for the seismic imaging procedures.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): F.L. Sun, C.Y. Dong, Y.H. Wu, Y.P. Gong A novel fast direct solver based on isogeometric boundary element method (IGABEM) is presented for solving 3D potential problems, which uses the hierarchical off-diagonal low-rank (HODLR) matrix structure arising from the discretization of boundary integral equations. Since the HODLR matrix can be factored into the product form of some diagonal blocks, we can use the Sherman–Morrison–Woodbury formula to solve the inverse of a HODLR matrix efficiently. For large scale problems, an accelerated adaptive cross approximation algorithm is developed to decompose the off-diagonal submatrices. In numerical implementation, bivariate NURBS basis functions are used to describe the geometry. Meanwhile, the same NURBS basis functions are also used to approximate the unknown boundary quantities. The present method is applied to some numerical examples, including an infinite space containing twenty spherical cavities. The numerical results clearly show that the fast direct solver developed in the paper can obtain accurate results with less CPU time.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Peiting Gao, Chuanjiang He, Yang Liu An adaptive class of conjugate gradient methods is proposed in this paper, which all possess descent property under strong-wolfe line search. The adaptive parameter in the search direction is determined by minimizing the distance between relative matrix and self-scaling memoryless BFGS update by Oren in the Frobenius norm. Two formulas of the adaptive parameter are further obtained, which are presented as those given by Oren and Luenberger (1973/74) and respectively Oren and Spedicato (1976). By projection technology, two adaptive projection algorithms are developed for solving monotone nonlinear equations with convex constraints. Some numerical comparisons show that these two algorithms are efficient. Last, the proposed algorithms are used to recover a sparse signal from incomplete and contaminated sampling measurements; the results are promising.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): Talha Achouri A conservative finite difference scheme is presented for solving the two-dimensional fourth-order nonlinear wave equation. The existence of the numerical solution of the finite difference scheme is proved by Brouwer fixed point theorem. With the aid of the fact that the discrete energy is conserved, the finite difference solution is proved to be bounded in the discrete L∞−norm. Then, the difference solution is shown to be second order convergent in the discrete L∞−norm. A numerical example shows the efficiency of the proposed scheme.

Abstract: Publication date: 15 October 2019Source: Applied Mathematics and Computation, Volume 359Author(s): A. Pratap, R. Raja, J. Cao, C.P. Lim, O. Bagdasar This article, we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous neuron activation functions (FCGNNDDs). First, under the framework of Filippov theory and differential inclusion theoretical analysis, the global existence of Filippov solution for FCGNNDDs is studied by means of the given growth condition. Second, by virtue of suitable Lyapunov functional, Young inequality and comparison theorem for fractional order delayed linear system, some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations. Third, the global asymptotic synchronization condition for FCGNNDDs is obtained based on the pinning control. At last, two numerical simulations are given to verify the theoretical findings.

Abstract: Publication date: Available online 29 March 2019Source: Applied Mathematics and ComputationAuthor(s): Qiang Li, Tong Zhang, Jinyun Yuan In the present study, the polymer crystal growth under the flow field is numerically simulated by using a coupled phase field (PF) and lattice Boltzmann (LB) method. Firstly, the phase field method is presented to capture the growth interface of polymer crystals, including the common morphologies of spherulite and shish-kebab crystallites. Then the lattice Boltzmann method is introduced to solve the viscous non-Newtonian flows of the polymer melt, where the half-way bounce back boundary condition is imposed with the aid of shape level-set (LS) function which is used to represent the crystal interface at each time. At last, the crystal growth for spherulites and shish-kebab crystallites under flow field is simulated by using the coupled PF–LB method, where the cross-WLF model is chosen to describe the melt viscosity. The effects of the flow velocity on the crystal morphologies, including single and multiple spherulite and shish-kebab crystallites, are analyzed in detail. The numerical results show that the flow velocity has an important impact on the crystal morphologies, and the crystals grow more faster towards the upstream direction, especially in the single and multi spherulites growth process.