Persistence and global stability of bazykin predator-prey model with beddington-deangelis response function

Sahabuddin Sarwardi, Mainul Haque, Prashanta Kumar Mandal

Research output: Journal PublicationArticlepeer-review

37 Citations (Scopus)

Abstract

In this article, a predator-prey model of Beddington-DeAngelis type with discrete delay is proposed and analyzed. The essential mathematical features of the proposed model are investigated in terms of local, global analysis and bifurcation theory. By analyzing the associated characteristic equation, it is found that the Hopf bifurcation occurs when the delay parameter τ crosses some critical values. In this article, the classical Bazykin's model is modified with Beddington-DeAngelis functional response. The parametric space under which the system enters into Hopf bifurcation for both delay and non-delay cases are investigated. Global stability results are obtained by constructing suitable Lyapunov functions for both the cases. We also derive the explicit formulae for determining the stability, direction and other properties of bifurcating periodic solutions by using normal form and central manifold theory. Our analytical findings are supported by numerical simulations. Biological implication of the analytical findings are discussed in the conclusion section.

Original languageEnglish
Pages (from-to)189-209
Number of pages21
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 2014
Externally publishedYes

Keywords

  • Delay
  • Ecological models
  • Global stability
  • Hopf bifurcation
  • Local stability
  • Numerical simulation
  • Permanence
  • Population models

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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