Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (3): 495-501.doi: 10.3969/j.issn.1005-3085.2022.03.013

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Stability and Hopf Bifurcation of a Reaction Diffusion Predator-prey Model with Prey Fear and Refuge

CHEN Qingwan,   LIU Wenqing   

  1. College of General Education, Minnan Science and Technology Institute, Quanzhou 362300
  • Online:2022-06-15 Published:2022-08-15
  • Supported by:
    The Education and Scientific Research Project for Young and Middle-aged Teachers in Fujian Province (JAT210616;JAT191035; JAT191044); the Project of the 14$^{\rm th}$ Five-year Plan of Education Science in Fujian Province (FJJKBK21-100).

Abstract:

Both fear factors and prey refuge have important effects in predation on the ecos-ystems. A class of reaction diffusion predator-prey models with fear effect and prey refuge is studied. We first provide the local asymptotic stability of the equilibrium point by using the linearization method and local bifurcation theory. Next, the existence of Hopf bifurcation and limit cycle is examined by choosing the ratio of un-protected prey as the bifurcation parameter. The results show that the existence of the refuge leads to Hopf bifurcation and spatially homogeneous periodic solution, and the addition of diffusion leads to new Hopf bifurcation points and inhomogeneous periodic solutions. This shows that the biological population can coexist by setting up an appropriate prey refuge or reducing the diffusion of predators. Finally, the conclusions are verified through numerical simulation.

Key words: fear factor, refuge, Hopf bifurcation, stability

CLC Number: