International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Full Length Research Paper

Hopf bifurcation analysis of a food web of four species

Zhouchao Wei1* and Li Li2
1School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, PR China. 2Institute of Applied Mycology, Huazhong Agricultural University, Wuhan, 430070, PR China.  
Email: [email protected]

  •  Accepted: 15 December 2011
  •  Published: 09 January 2012



 In this paper, we analyze the Hopf bifurcation of basic food web of four species based on standard normal form theory. The basic model we consider is owed to a bottom prey X, two competing predators Y and Z on X, and a super-predator W only on Y. It is found that periodic solutions arise from the main parameter values  and  through through a Hopf bifurcation point. The direction and type of the Hopf bifurcation involved as well as the parameter values also are determined.


Key words: Chaos, bifurcation analysis, food web, prey-predator, four-dimensional.