Spatiotemporal dynamics of a diffusive predator–prey model with fear effect
Articles
Jia Liu
Jiangsu Vocational College of Electronics and Information
Yun Kang
Arizona State University
https://orcid.org/0000-0001-5448-7609
Published 2022-05-14
https://doi.org/10.15388/namc.2022.27.27535
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Keywords

diffusion
stability
fear effect
predator–prey model

How to Cite

Liu, J. and Kang, Y. (2022) “Spatiotemporal dynamics of a diffusive predator–prey model with fear effect”, Nonlinear Analysis: Modelling and Control, 27(5), pp. 841–862. doi:10.15388/namc.2022.27.27535.

Abstract

This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system.

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