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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

Phase Portraits, Hopf Bifurcations and Limit Cycles of the Ratio Dependent Holling-Tanner Models for Predator-prey Interactions

Journal of Applied Nonlinear Dynamics 5(3) (2016) 283--304 | DOI:10.5890/JAND.2016.09.003

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

In this paper we consider a ratio dependent Holling Tanner predator prey model with type II functional responses. We analyzed the local stability, phase portraits, existence and uniqueness of stable limit cycles and Hopf bifurcation. The ranges of the parameter involved are provided under which the unique interior equilibrium can be determined for a stable (or an unstable) node or focus without diffusion. Furthermore the Turing instability analysis of the system with diffusion are studied. Numerical simulations using MATLAB are carried out to demonstrate the theoretical results obtained.

Acknowledgments

The authors are thankful to the referees for the improvement of the paper.They are also thankful to DRDO, New Delhi for its financial support to carryout the research.

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