Global dynamics of a predator-prey system with density-dependent mortality and ratio-dependent functional response

Xin Jiang, Zhikun She, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the global dynamics of a density-dependent predator-prey system with ratio-dependent functional response. The main fea- tures and challenges are that the origin of this model is a degenerate equilibrium of higher order and there are multiple positive equilibria. Firstly, local quali- tative behavior of the system around the origin is explicitly described. Then, based on the dynamics around the origin and other equilibria, global qualitative analysis of the model is carried out. Finally, the existence of Bogdanov-Takens bifurcation (cusp case) of codimension two is analyzed. This shows that the system undergoes various bifurcation phenomena, including saddle-node bifur- cation, Hopf bifurcation, and homoclinic bifurcation along with di_erent topo- logical sectors near the degenerate origin. Numerical simulations are presented to illustrate the theoretical results.

Original languageEnglish (US)
Pages (from-to)1967-1990
Number of pages24
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume26
Issue number4
DOIs
StatePublished - Apr 2021

Keywords

  • Bogdanov-Takens bifurcation
  • Density-dependent mortality
  • Global dynamics
  • Predator-prey system
  • Ratio-dependent

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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