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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamical Complexity and Numerical Bifurcation Analysis of a Reaction-Diffusion Predator-Prey System

Journal of Applied Nonlinear Dynamics 9(2) (2020) 323--337 | DOI:10.5890/JAND.2020.06.012

Z. Lajmiri$^{1}$, I. Orak$^{1}$, R. Khoshsiar$^{2}$, P. Azizi$^{3}$

$^{1}$ Sama technical and vocatinal training college Islamic Azad University Izeh Branch, Izeh, Iran

$^{2}$ Department of Applied Mathematics and Computer Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

$^{3}$ Student of Applied Mathematics, Shahrekord University, P.O. Box 115, Shahrekord, Iran

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Abstract

In this paper, we consider a diffusive predator-prey system with modified Holling-Tanner functional response under homogeneous Neumann boundary condition . Dynamics of the system is very sensitive to the variation of the initial conditions. We determine stability and dynamical behaviors of the equilibrium of this system. The dynamical behaviors consist of Andronov-Hopf bifurcation, limit cycles and Bogdanov-Takens bifurcations. Numerical simulation results are given to support our theoretical results.

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