Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2753

Full Length Research Paper

Bifurcation and chaos of a three-species Lotka-Volterra food-chain model with spatial diffusion and time delays

  Liying Cai*, Xisheng Jia, Jianmin Zhao and Zhonghua Cheng
Department of Equipment Command and Management, Mechanical Engineering College, Shijiazhuang 050003, China.
Email: [email protected]

  •  Accepted: 11 November 2010
  •  Published: 31 December 2010

Abstract

 

 

In this paper, a three-species Lotka-Volterra food-chain model with spatial diffusion and time delays is investigated. We first analyze the local stability of the steady states and the existence of Hopf bifurcation to this system under homogeneous Neumann boundary conditions. We consider the effects of impulses on the dynamics of the above food-chain model without spatial diffusion. Numerical simulations show that the system with constant periodic impulsive perturbations admits rich complex dynamics.

 

Key words: Hopf bifurcation, food chain, reaction diffusion, delay, stability, chaos.