Dynamic Analysis Of A Class Of Predator-prey System For Cooperative Foraging With Delay And Diffusion

In this thesis,we study a class of gray Wolf-Tibetan antelope predator-prey model,which adds a cooperative item to the predator group attack.At the same time,considering the Smith-type growth of prey population due to the limitation of resources and environment,we introduce the diffusion term and digestion time delay into the system to establish a predator-prey system with Smith growth and hunting cooperation.Firstly,for the local model,the cooperative coefficient is selected as the control parameter to analyze the characteristic roots.The existence of the equilibrium point of the predation system is discussed and the sufficient conditions for the local asymptotic stability of the equilibrium point are given.Our analytical results show that hunting cooperation can be beneficial to the predator population.However,as the cooperation coefficient increases,hunting cooperation can also destabilize the model.Secondly,for the reaction-diffusion model,we analyze the diffusion-driven Turing instability of the positive equilibria.In particular,it should be noted that the model does not produce Turing instability without hunting cooperation,which may lead to Turing instability.Then,for the time-spatial model,taking the digestion delay as the branching parameter,the conditions of Hopf bifurcation existence are discussed,and using the central manifold theorem and the canonical form method,the properties of Hopf bifurcation such as the direction and stability of bifurcating periodic solutions are studied.Finally,a numerical simulation is presented to demonstrate the reliability of the theoretical analysis that the cooperative hunting behavior of predators and the digestive delay affect the dynamic behavior of the system.