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

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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.

Keywords

predator-prey model / delay / Hopf bifurcation / Crowley-Martin functional response

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