Hopf bifurcation analysis in delayed predator-prey models with the Crowley-Martin functional response

Shuang Guo; Xing Qiao; Dan Ma; Shuang Guo; Xing Qiao; Dan Ma

doi:10.3934/era.2026245

Electronic Research Archive

2026, Volume 34, Issue 8: 5478-5495. doi: 10.3934/era.2026245

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Research article

Hopf bifurcation analysis in delayed predator-prey models with the Crowley-Martin functional response

School of Mathematical Sciences, Daqing Normal University, Daqing 163712, China

Received: 03 March 2026 Revised: 29 May 2026 Accepted: 08 June 2026 Published: 30 June 2026

A class of delayed predator-prey models with the Crowley-Martin functional response was investigated in this study. First, the conditions for the stability of the coexistence equilibrium were obtained. Second, by applying the normal form method and the center manifold theorem, the conditions for the occurrence of a Hopf bifurcation induced by the time delay were established, and the direction of the Hopf bifurcation was determined. Finally, numerical simulations were conducted to illustrate the theoretical results. The findings provided insights into the effects of time delay on stability and oscillatory behavior in predator-prey interactions, which are significant for understanding population dynamics in ecology.
- predator-prey model,
- delay,
- Hopf bifurcation,
- Crowley-Martin functional response
Citation: Shuang Guo, Xing Qiao, Dan Ma. Hopf bifurcation analysis in delayed predator-prey models with the Crowley-Martin functional response[J]. Electronic Research Archive, 2026, 34(8): 5478-5495. doi: 10.3934/era.2026245

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Abstract

A class of delayed predator-prey models with the Crowley-Martin functional response was investigated in this study. First, the conditions for the stability of the coexistence equilibrium were obtained. Second, by applying the normal form method and the center manifold theorem, the conditions for the occurrence of a Hopf bifurcation induced by the time delay were established, and the direction of the Hopf bifurcation was determined. Finally, numerical simulations were conducted to illustrate the theoretical results. The findings provided insights into the effects of time delay on stability and oscillatory behavior in predator-prey interactions, which are significant for understanding population dynamics in ecology.

References

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