The Existence of Hopf Bifurcation for a Delayed Holling-Tanner Type Predator-Prey Model
Canadian Mathematical Bulletin, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.4153/s0008439525101598
- Journal Name: Canadian Mathematical Bulletin
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: discrete delay, Hopf bifurcation, Predator-prey system, stability
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
In this study, a Holling–Tanner type predator–prey model with a discrete time delay is investigated, where the functional response of the predator dynamics is ratio-dependent. We first analyze the local stability of the equilibrium point and examine the existence of Hopf bifurcations. The Hopf bifurcation, also known as the Poincare–Andronov–Hopf bifurcation, is named after the French mathematician Jules Henri Poincare, the Russian mathematician Alexander A. Andronov, and the German mathematician Heinz Hopf, whose fundamental contributions laid the foundation of this theory. By treating the delay parameter τ as the bifurcation parameter, we show that a Hopf bifurcation occurs when the delay crosses certain critical values. Finally, numerical simulations are carried out to support and illustrate our theoretical results.