HOPF BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER HOLLING-TANNER PREDATOR-PREY MODEL WITH TIME DELAY


Celik C., DegerlI K.

ANZIAM JOURNAL, vol.64, pp.23-39, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64
  • Publication Date: 2022
  • Doi Number: 10.1017/s1446181122000025
  • Journal Name: ANZIAM JOURNAL
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, INSPEC, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.23-39
  • Keywords: fractional-order, time-delay, Hopf bifurcation, predator-prey system, STABILITY, SYSTEM, DISCRETE

Abstract

We study a fractional-order delayed predator-prey model with Honing -Tanner-type functional response. Mainly, by choosing the delay time tau as the bifurcation parameter, we show that Hopf bifurcation can occur as the delay time tau passes some critical values. The local stability of a positive equilibrium and the existence of the Hopf bifurcations are established, and numerical simulations for justifying the theoretical analysis are also presented.