Hopf bifurcation analysis of the delayed diffusive predator-prey model with harvesting terms

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Abstract

This paper studied a delayed diffusive predator-prey model with predator and prey harvesting terms. The existence of constant steady-state solutions and Hopf bifurcation were analyzed. Then by applying the central manifold theorem and the normal form method, the direction of the Hopf bifurcation and stability of the bifurcating period solution were studied. Numerical simulations were conducted to confirm the accuracy of the proposed theory. In addition, taking the predator-prey relationship between sharks and tuna as an example, this study investigated the impact of predator harvesting coefficients on the constant steady-state solutions of the system and the time required for the system to reach stability.

Keywords

predator-prey model / delay / harvesting term / Hopf bifurcation

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