Authors:Y. Sofuoglu; N. Ozalp Pages: 1 - 9 Abstract: Abstract A fractional order model of a population with one bilingual and two unilingual components, in which conversion from dominant unilingual to bilingual doesn’t exist is studied. Equilibrium points are found, criteria for the existence and the stability of the positive equilibrium are then investigated. Also, numerical solutions for an example of the fractional order system are obtained by transforming the fractional system to the corresponding integer order one. PubDate: 2017-01-01 DOI: 10.1007/s12591-015-0239-9 Issue No:Vol. 25, No. 1 (2017)

Authors:Jagadish Singh; Nakone Bello Pages: 29 - 37 Abstract: Abstract This paper studied the motion of a test particle in the vicinity of the triangular points \(L_{4,5}\) , by considering both primaries as sources of radiation in the framework of the relativistic restricted three-body problem. It is found that the positions and stability of the triangular point are affected by both the relativistic and mass reduction factors. As an application, this model could be the study of the motion of a dust grain particle near luminous binary systems. PubDate: 2017-01-01 DOI: 10.1007/s12591-014-0236-4 Issue No:Vol. 25, No. 1 (2017)

Authors:Dan Goreac; Oana-Silvia Serea Pages: 83 - 100 Abstract: Abstract In this short paper we prove that, in the framework of continuous control problems for piecewise deterministic Markov processes, the existence of a uniform limit for discounted value functions as the discount factor vanishes implies (without any further assumption) the uniform convergence of the value functions with long run average cost as the time horizon increases to infinity. The two limit values coincide. We also provide a converse Tauberian result for a particular class of systems with Poisson-triggered jump mechanism. We exhibit a very simple example in which the dynamics are not dissipative, nevertheless discounted values converge uniformly to a non-constant limit function. PubDate: 2017-01-01 DOI: 10.1007/s12591-015-0245-y Issue No:Vol. 25, No. 1 (2017)

Abstract: Abstract In this paper, we take up the existence and the asymptotic behavior of positive and continuous solutions to the following coupled fractional differential system $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle D^{\alpha } u=a(x)\displaystyle u^{p }\displaystyle v^{r}\quad \text { in }(0,1) , \\ \displaystyle D^{\beta } v=b(x)\displaystyle u^{s }\displaystyle v^{q}\quad \text { in }(0,1) , \\ u(0)= u(1)= D^{\alpha -3}u(0)= u^{\prime }(1)=0,\\ v(0)= v(1)= D^{\beta -3}v(0)= v^{\prime }(1)=0, \end{array} \right. \end{aligned}$$ where \( \alpha , \beta \in (3,4]\) , \(p, q\in (-1,1)\) , \(r, s\in \mathbb {R}\) such that \((1- p )(1- q )- rs > 0\) , D is the standard Riemann–Liouville differentiation and a, b are nonnegative and continuous functions in (0, 1) allowed to be singular at \(x=0\) and \(x=1\) and they are required to satisfy some appropriate conditions related to Karamata regular variation theory. PubDate: 2017-03-25

Abstract: Abstract This paper is devoted to the study of the linearization problem of fifth-order ordinary differential equations by means of contact transformations. The necessary and sufficient conditions for linearization are obtained. The procedure for obtaining the linearizing transformations is provided in explicit form. Examples demonstrating the procedure of using the linearization theorems are presented. PubDate: 2017-03-21

Authors:Şeyma Bayrak; Philipp Hövel; Vesna Vuksanović Abstract: Abstract This study combines modeling of neuronal activity and networks derived from neuroimaging data in order to investigate how the structural organization of the human brain affects the temporal dynamics of interacting brain areas. The dynamics of the neuronal activity is modeled with FitzHugh–Nagumo oscillators and the blood-oxygen-level-dependent (BOLD) time series is inferred via the Balloon–Windkessel hemodynamic model. The simulations are based on anatomical probability maps between considered brain regions of interest. These maps were derived from diffusion-weighted magnetic resonance imaging measurements. In addition, the length of the fiber tracks allows for inference of coupling delays due to finite signal propagation velocities. We aim to investigate (i) graph-theoretical properties of the network topology derived from neuroimaging data and (ii) how randomization of structural connections influences the dynamics of neuronal activity. The network characteristics of the structural connectivity data are compared to density-matched Erdős–Rényi random graphs. Furthermore, the neuronal and BOLD activity are modeled on both empirical and random (Erdős–Rényi type) graphs. The simulated temporal dynamics on both graphs are compared statistically to capture whether the spatial organization of these network affects the modeled time series. Results support previous findings that key topological network properties such as small-worldness of our neuroimaging data are distinguishable from random networks. We also show that simulated BOLD activity is affected by the underlying network topology and the strength of connections between the network nodes. The difference of the modeled temporal dynamics of brain networks from the dynamics on randomized graphs suggests that anatomical connections in the human brain together with dynamical self-organization are crucial for the temporal evolution of the resting-state activity. PubDate: 2017-03-11 DOI: 10.1007/s12591-017-0354-x

Authors:Argha Mondal; Chinmoy Paul; Gajendra Kumar Vishwakarma; Ranjit Kumar Upadhyay Abstract: Abstract This article reports a method for the estimation of parameters of a 3D Hindmarsh Rose neural model under a noisy measurement. Estimation procedure is based on reparametrization of the 3D model in a linear form. Method of least square has been used to estimate the biophysical parameters of the model. It is known that the presence of unavoidable noise effects the estimation procedure. To reduce the influence of noise to a certain extent, a denoising algorithm based on local projection is considered. Estimation procedure has been derived both in noisy and denoised condition to present the effectiveness of the algorithm. The denoising technique has been applied to reduce the influence of noisy stimuli in an experimentally collected EEG data set and the results are presented in terms of reduction in variance level. The effectiveness of the method is presented using analytical/mathematical and simulation results. PubDate: 2017-03-07 DOI: 10.1007/s12591-017-0355-9

Authors:Rukkayat Suleiman; Aishetu Umar; Jagadish Singh Abstract: Abstract The positions and stability of the collinear equilibrium points in the photogravitational ER3BP with zonal harmonics of the secondary is investigated. The effects of the perturbing forces: - oblateness, eccentricity and radiation pressure—on the positions and stability of collinear points \((L_{1,2,3})\) of an infinitesimal mass in the framework of the photogravitational ER3BP with zonal harmonics of the secondary are established. These effects on the positions of the binary systems Zeta Cygni, 54 Piscium, Procyon A/B and Regulus A are shown graphically and numerically from the analytic results obtained. It is observed that as the zonal harmonic \(J_{4}\) and eccentricity e increase, the collinear points shift towards the origin, while the reverse is observed with increase in the semi-major axis. The stability behavior however is unaffected by the introduction of these parameters, the collinear points remain linearly unstable. PubDate: 2017-03-06 DOI: 10.1007/s12591-017-0352-z

Authors:Mohammad Shahrouzi Abstract: Abstract This article is devoted to the study blow up of solutions to a quasilinear inverse source problem with memory and damping terms. We obtain sufficient conditions on initial functions for which the solutions blow up in a finite time. Estimates of the lifespan of solutions are also given. PubDate: 2017-03-03 DOI: 10.1007/s12591-017-0356-8

Authors:Francisco J. Solis; Alina Sotolongo Abstract: Abstract In this work we complete the analysis of convergence for nonhyperbolic fixed points of two dimensional discrete dynamical systems. We analyze all different scenarios of systems with isolated equilibria whose linearized part has eigenvalues of norm one, except for those with real eigenvalues equal to one, which have been studied previously. We also include the non-diagonalizable case and the case of mixing eigenvalues, where only one real eigenvalue has absolute value equal to one. Different techniques have been applied depending on the hyperbolic scenario. Finally, many two dimensional examples are presented in order to illustrate the diverse orbit behaviors and the number of iterations required to converge. PubDate: 2017-03-01 DOI: 10.1007/s12591-017-0353-y

Authors:Yonggang Ma; Qimin Zhang; Xining Li Abstract: Abstract This paper conducts a dissipative analysis for comprehensive genetic regulatory network models with fractional Brownian motion (fBm), diffusion-reaction processes, Markovian jump and time-varying delay. By constructing an appropriate Lyapunov–Krasovskii functional, utilizing linear matrix inequality (LMI) technique and stochastic theory, several sufficient conditions of global dissipativity and strictly \(({{\mathscr {Q}}},{{\mathscr {S}}},{{\mathscr {R}}})\) - \(\gamma \) -dissipativity of the solution are established. Moreover, the global attractive sets which are positive invariant are obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. PubDate: 2017-02-23 DOI: 10.1007/s12591-017-0349-7

Authors:Tania Bose; Minto Rattan Abstract: Abstract An attempt has been made to model steady-state creep for thermally graded rotating disc made of linearly varying functionally graded material. The stress and strain rate distributions have been calculated for the discs rotating at linearly/parabolically decreasing temperatures using threshold stress based creep law and von Mises’ yield criterion. Further, these results are compared with the disc operating at uniform temperature throughout the radial distance. The results are displayed and compared graphically in designer friendly format for the said temperature profiles. The analysis indicates that stress in composite disc operating under thermal gradient slightly increases as compared to disc operating under constant temperature. However, the strain rate developed near the inner radius in the disc rotating at uniform temperature is lower in comparison to disc having linear/parabolic thermal gradations; whereas the disc operating at uniform temperature shows higher strain rate as compared to disc having linear/parabolic thermal gradations near the outer radius. It is observed that for the disc having thermal gradation the steady state creep rates show less deviation as compared to the disc operating under uniform temperature throughout the radial distance. PubDate: 2017-02-15 DOI: 10.1007/s12591-017-0350-1

Authors:Cheng Chen; Yao-Lin Jiang Abstract: Abstract In this paper combined KdV–mKdV equation is deeply explored. The optimal system of one-dimensional subalgebra is determined. Similarity reductions of combined KdV–mKdV equation are performed and group invariant solutions are given under optimal system of subgroups. Some special exact solutions are obtained by the simplest equation method. Moreover the equation is shown to be self-adjoint and we construct conservation laws of combined KdV–mKdV equation. PubDate: 2017-02-15 DOI: 10.1007/s12591-017-0351-0

Authors:Ágnes Bodó; Péter L. Simon Abstract: Abstract The pairwise ODE model for SIS epidemic propagation on an adaptive network with link number preserving rewiring is studied. The model, introduced by Gross et al. (Phys Rev Lett 96:208701, 2006), consists of four ODEs and contains three parameters, the infection rate \(\tau \) , the recovery rate \(\gamma \) and the rewiring rate w. It is proved that transcritical, saddle-node and Andronov–Hopf bifurcations may occur. These bifurcation curves are determined analytically in the \((\tau , w)\) parameter plane by using the parametric representation method, together with the two co-dimensional Takens–Bogdanov bifurcation point. It is shown that this parameter plane is divided into four regions by the above bifurcation curves. The possible behaviours are as follows: (a) globally stable disease-free steady state, (b) stable disease-free steady state with two unstable endemic equilibria and a stable periodic orbit, (c) stable disease-free steady state with a stable and an unstable endemic equilibrium and (d) a globally stable endemic equilibrium. Numerical evidence is shown that homoclinic bifurcation, giving rise to an unstable periodic orbit, and cycle-fold bifurcation also occur. PubDate: 2017-02-10 DOI: 10.1007/s12591-017-0348-8

Authors:Kristen Abernathy; Zachary Abernathy; Arden Baxter; Meghan Stevens Abstract: Abstract In this paper, we present a system of five ordinary differential equations which consider population dynamics among cancer stem cells, tumor cells, and healthy cells. Additionally, we consider the effects of excess estrogen and the body’s natural immune response on the aforementioned cell populations. Employing a variety of analytical methods, we study the global dynamics of the full system, along with various submodels. We find sufficient conditions on parameter values to ensure cancer persistence in the absence of immune cells, and cancer eradication when an immune response is included. We conclude with a discussion on the biological implications of the resulting global dynamics. PubDate: 2017-01-20 DOI: 10.1007/s12591-017-0346-x

Authors:Vy Khoi Le Abstract: Abstract In this paper, we study variational inequalities of the form $$\begin{aligned} \left\{ \begin{array}{l} \langle {\mathcal {A}}(u), v-u \rangle + \langle {{\mathcal {F}}}(u), v-u \rangle + J(v) - J(u) \ge 0,\quad \forall v\in X \\ u\in X, \end{array} \right. \end{aligned}$$ where \({\mathcal {A}}\) and \({{\mathcal {F}}}\) are multivalued operators represented by integrals, J is a convex functional, and X is a Sobolev space of variable exponent. The principal term \({\mathcal {A}}\) is a multivalued operator of Leray–Lions type. We concentrate on the case where \({{\mathcal {F}}}\) is given by a multivalued function \(f = f(x,u,\nabla u)\) that depends also on the gradient \(\nabla u\) of the unknown function. Existence of solutions in coercive and noncoercive cases are considered. In the noncoercive case, we follow a sub-supersolution approach and prove the existence of solutions of the above inequality under a multivalued Bernstein–Nagumo type condition. PubDate: 2017-01-16 DOI: 10.1007/s12591-017-0345-y

Authors:Murat Babaarslan; Mustafa Kayacik Abstract: Abstract In the present paper, we investigate the differential equations of the space-like loxodromes on the helicoidal surfaces having space-like meridians and time-like meridians, respectively in Minkowski 3-space. Also we illustrate our main results by using Mathematica. PubDate: 2017-01-07 DOI: 10.1007/s12591-016-0343-5

Authors:C. Maji; D. Kesh; D. Mukherjee Abstract: Abstract This paper deals with predator-prey-pathogen interaction where predator influences the transmission rate of the infection in its prey. It is assumed that predator consumes infected prey only. The main results address the existence of interior equilibrium point and its stability. Also we derive the condition for persistence of the system. Bifurcation at the coexistence equilibrium point is established. Lastly, the condition for non-existence of closed orbits is found. Some numerical simulations illustrate the obtained results. PubDate: 2017-01-07 DOI: 10.1007/s12591-016-0342-6

Authors:P. D. N. Srinivasu; D. K. K. Vamsi; I. Aditya Abstract: Abstract Ecological and biological conservation of living systems has been an active area of research over the years by agriculturalists, biologists and mathematicians. One of the studies involves additional food supplement feeding (also called as diversionary feeding) for the purpose of biological (wildlife in some cases) conservation. The idea in this approach is to distract (thereby supplement) the wildlife from predating upon the other species with the end goal of wildlife conservation. On the other hand in agricultural entomology, insect control and optimization, additional food is supplemented as a tool for effective pest control thereby achieving the biological control. The study of these ecosystems is usually done using the predator–prey systems. In nature, we find situations wherein the group defense (toxicity) of the prey reduces the predator’s predation rate. This type of behaviour of the prey is also known as inhibitory effect of the prey. Biological conservation of such predator prey systems in the presence of additional food supplements is quite challenging and interesting. In this paper, we consider an additional food provided predator–prey system which is a variation of the standard predator–prey model in the presence of the inhibitory effect of the prey. The predators functional response is assumed to be of Holling type IV (considering the inhibitory effect). This model is analyzed to understand the inherent dynamics of the system. The findings suggest that the quality and quantity of additional food provided to the predators, play a very significant role in determining the eventual state of the ecosystem. The outcomes of the analysis suggests eco friendly strategies to eco-managers for biological conservation of living systems. PubDate: 2017-01-06 DOI: 10.1007/s12591-016-0344-4