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Nonlinear Dynamics

, Volume 94, Issue 4, pp 2901–2918 | Cite as

Bifurcation analysis of a diffusive predator–prey system with nonmonotonic functional response

  • Bounsanong Sounvoravong
  • Jianping Gao
  • Shangjiang Guo
Original Paper
  • 138 Downloads

Abstract

In this paper, a diffusive predator–prey model with nonmonotonic functional response is investigated. The stability of the positive spatially homogeneous steady states and bifurcations of spatially homogeneous/nonhomogeneous time-periodic solutions as well as steady-state solutions are studied. In particular, the formulas determining the direction and the stability of the bifurcating periodic solutions are obtained. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulations.

Keywords

Diffusion Kinetic system Hopf bifurcation Steady-state bifurcation 

Mathematics Subject Classification

35J20 35J60 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Bounsanong Sounvoravong
    • 1
  • Jianping Gao
    • 1
  • Shangjiang Guo
    • 1
  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaPeople’s Republic of China

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