Dynamical behaviour of an intraguild predator-prey model with prey refuge and hunting cooperation

An intraguild predator-prey model including prey refuge and hunting cooperation is investigated in this paper. First, for the corresponding ordinary differential equation model, the existence and stability of all equilibria are given, and the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are investigated. Then, for partial differential equation model, the diffusion-driven Turing instability is obtained. What is more, the existence and non-existence of the non-constant positive steady state of the reaction-diffusion model are established by the Leray-Schauder degree theory and some priori estimates. Next, some numerical simulations are performed to support analytical results. The results showed that prey refuge can change the stability of model and even have a stabilizing effect on this model, meanwhile the hunting cooperation can make such model without diffusion unstable, but make such model with diffusion stable. Lastly, a brief conclusion is concluded in the last section.

Automated summary

In this paper, an intraguild predator-prey model with prey refuge and hunting cooperation is investigated. The existence and stability of all equilibria of the corresponding ordinary differential equation model are analyzed, along with the presence of Hopf bifurcation and the direction and stability of bifurcating periodic solutions. Furthermore, a diffusion-driven Turing instability is obtained for the partial differential equation model. The Leray-Schauder degree theory and some priori estimates are employed to establish the existence and non-existence of the non-constant positive steady state of the reaction-diffusion model. Numerical simulations are performed to support the analytical results. The findings demonstrate that prey refuge can alter the stability of the model and even have a stabilizing effect, while hunting cooperation can make the model without diffusion unstable but make the model with diffusion stable. A succinct conclusion is provided in the final section.