Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (2): 358-371.

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Hopf Bifurcation of Delayed Density-Dependent Predator-Prey Model

Haiyin Li()   

  1. Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046
  • Received:2017-08-09 Online:2019-04-26 Published:2019-05-05
  • Supported by:
    the NSFC(61640315);the Key Scientific Research Project of Henan Higher Education Institutions(18A110012)

Abstract:

In this paper, we investigate stability and Hopf bifurcation of a delayed density-dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered such that the studied predator-prey system conforms to the realistically biological environment. Firstly, stability transformation of the system was given to prepare for discussion of bifurcating periodic solution. Secondly, we discussed properties of Hopf bifurcation about bifurcating direction, stability and period by center manifold theorem and normal form theory. Finally, an example with numerical simulations is given to illustrate stability transformation and Hopf bifurcation of the system.

Key words: Density dependent predator, Prey-predator system, Time delay, Hopf bifurcation

CLC Number: 

  • O193
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