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)

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

Dynamics of a Modified Leslie-Gower Model with Crowley-Martin Functional Response and Prey Harvesting

Journal of Applied Nonlinear Dynamics 8(4) (2019) 621--636 | DOI:10.5890/JAND.2019.12.008

R. Sivasamy$^{1}$, K. Sathiyanathan$^{1}$, K. Balachandran$^{2}$

$^{1}$ Department of Mathematics, SRMV College of Arts and Science, Coimbatore - 641020, India

$^{2}$ Department of Mathematics, Bharathiar University, Coimbatore - 641046, India

Abstract

In this paper, dynamics of modified Leslie-Gower predator-prey model with Crowley-Martin functional response and nonlinear prey harvesting is discussed. We discuss the permanence analysis and local stability of all possible equilibrium points. Also we derive the conditions for occurrence of Hopf bifurcation around positive equilibrium point and its stability. The global stability of positive equilibrium point is derived by using proper Lyapunov functional. Further the Hutchinson’s delay is introduced to utilize the fact that prey takes some time lag to convert the food into its growth. It is noted that the Hopf bifurcation occurs when the time lag parameter τ crosses its critical value. The proposed theoretical results are verified with the help of numerical simulations.

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