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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Bifurcation and Stability Analysis of a Diffusive Predator-Prey Model with Ratio-Dependent Type III Functional Response

Discontinuity, Nonlinearity, and Complexity 6(3) (2017) 393--407 | DOI:10.5890/DNC.2017.09.008

M. Sivakumar; K. Balachandran

DRDO-BU-CLS, Bharathiar University, Coimbatore - 641046, India.

Department of Mathematics, Bharathiar University, Coimbatore - 641046, India.

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Abstract

This paper is concerned with a diffusive Leslie-Gower predator-prey system with ratio dependent Holling type III functional response subject to Neumann boundary conditions. By linearizing the system at the positive constant steady-state solution and analyzing the associated characteristic equation in detail, local stability, existence of a Hopf bifurcation at the coexistence of the equilibrium and stability of bifurcating periodic solutions of the system in the absence of diffusion are studied. Furthermore, Turing instability and Hopf bifurcation analysis for the system with diffusion are studied. Finally, numerical simulations are provided in order to verify our theoretical results.

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