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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

Qualitative Analysis of a Modified Leslie-Gower Model with Gestation Delay

Journal of Applied Nonlinear Dynamics 10(3) (2021) 397--411 | DOI:10.5890/JAND.2021.09.004

R. Sivasamy , K. Nivethitha, S. Maheswari

Department of Science and Humanities, M.Kumarasamy College of Engineering, Tamil Nadu, India

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Abstract

This paper explores the qualitative analysis of a modified Leslie-Gower prey-predator model where the consumption rate of prey is by per capita predator according to Beddington-DeAngelis functional response. Moreover, time-lag $(\tau)$ is established to exploit a gestation period of predations. The permanence analysis of the proposed system is investigated. We study the local stability of the non-delayed model at all possible equilibrium points. It is demonstrated that the given model experiences Hopf bifurcation about the interior equilibrium point with respect to delay $\tau$. Thereafter the stability and direction of Hopf bifurcation are formulated through normal and center manifold theorems. The derived criteria are justified with the help of numerical simulations.

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