Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1980-1992.

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The Influence of Fear Effect on Stability Interval of Reaction-Diffusion Predator-Prey System with Time Delay

Yue Sun(),Daoxiang Zhang*(),Wen Zhou   

  1. School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241002
  • Received:2020-11-30 Online:2021-12-26 Published:2021-12-02
  • Contact: Daoxiang Zhang;
  • Supported by:
    the NSFC(11671013);the NSFC(11302002);the NSF of Anhui Province(2008085MA13)


This paper combines theoretical derivation and numerical simulation to study the dynamics of a delayed reaction-diffusion predator-prey model with fear effect. First, the existence and stability of the positive equilibrium point of the system are studied. Secondly, the Hopf bifurcation problem of the system is studied through linear stability analysis. The results show that the fear effect affects the Hopf bifurcation point, and then affects the stability interval of the system. Finally, the theoretical results are verified by numerical simulations, and the nonlinear relationship between the fear effect and the stability interval is found, that is, as the fear effect continues to increase, the system will change from a stable state to an unstable state, and then to a stable state.

Key words: Fear effect, Hopf bifurcation, Delay, Diffusion, Predator-prey system

CLC Number: 

  • O175.2