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Complex dynamics of COVID-19 mathematical model on Erdos-Rényi network

生物数学学报:英文版 2023年第5期16卷 193-215页

作者： Neriman kartal senol kartal Department of Science and Mathematics Education Faculty of Education Nevsehir Haci Bektas Veli University Nevsehir 50300Turkey

In this study,a conformable fractional order Lotka-Volterra predator-prey model that describes the COVID-19 dynamics is *** using a piecewise constant approximation,a discretization method,which transforms the conformable fractional-order differential equation into a difference equation,is *** conditions for ensuring the stability of the equilibrium points of the discrete system are determined by using Schur-Cohn *** analysis shows that the discrete system exhibits Neimark-Sacker bifurcation around the positive equilibrium point with respect to changing the parameter d and *** Lyapunov exponents show the complex dynamics of the discrete *** addition,the COVID-19 mathematical model consisting of healthy and infected populations is also studied on the Erdos Rényi *** the coupling strength reaches the critical value,then transition from nonchaotic to chaotic state is observed in complex dynamical ***,it has been observed that the dynamical network tends to exhibit chaotic behavior earlier when the number of nodes and edges *** these theoretical results are interpreted biologically and supported by numerical simulations.

关键词： Piecewise constant arguments difference equation stability Neimark-Sacker bifurcation complex network

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Multiple bifurcations in an early brain tumor model with piecewise constant arguments

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International Journal of Biomathematics 2018年第4期11卷 197-215页

作者： senol kartal Department of Science and Mathematics Education Nevsehir Haci Bektas Veli University Nevsehir 50300 Turkey

In this paper, a differential equation with piecewise constant arguments modeling an early brain tumor growth is considered. The discretization process in the interval t ∈ [ n , n + 1 ) leads to two-dimensional discrete dynamical system. By using the Schur–Cohn criterion, stability conditions of the positive equilibrium point of the system are obtained. Choosing appropriate bifurcation parameter, the existence of Neimark–Sacker and flip bifurcations is verified. In addition, the direction and stability of the Neimark–Sacker and flip bifurcations are determined by using the normal form and center manifold theory. Finally, the Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors of the system.

关键词：分叉常数脑肿瘤模特儿 Lyapunov 稳定性条件多重肿瘤生长

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