Dispersal Strategy Of An Intraguild Predation Model In Spatially Heterogeneous Environment

This dissertation focuses on the diffusion strategy of intraguild predation model with Holling-Ⅱ functional response function in spatially heterogeneous environment.The main results are as follows:In the first part,we discuss the uniform diffusion of predator and prey intraguild predation model.Firstly,we analyze the eigenvalue problems of linearized systems,and discuss the stability of trivial and semi-trivial solutions.Secondly,the stability conditions of the semi-trivial solutions are analyzed,and it is concluded that slow diffusion is conducive to the coexistence of species in the case of uniform diffusion.Finally,the existence of coexistence solutions is proved by the Leray-Schauder degree theory.In the second part,we mainly discuss the intraguild predation model in which the predator has starvation-driven diffusion and the prey has uniform diffusion.Firstly,we obtain the stability results of the system by linearization and eigenvalue problem analysis.Secondly,Leray-Schauder degree theory is used to discuss the existence of coexistence solutions;Finally,the stability results of starvation-driven diffusion system of the predator were compared with those of the system with uniform diffusion,and it was found that in the system with starvation-driven diffusion strategy of the predator,the survival of the predator was more likely when the prey dispersal much slower than that of the predator when the environment resources were sufficient.In the third part,we mainly discuss the intraguild predation model in which the predator has uniform diffusion and the prey has starvation-driven diffusion.Firstly,linearized systems at the trivial and semi-trivial solutions are derived,and the stability of the system is obtained by eigenvalue analysis.Secondly,the existence of coexistence solutions is studied by using Leray-Schauder degree theory;Finally,the stability results of starvationdriven diffusion system and the uniform diffusion system were compared and analyzed.It was found that the prey subject to starvation-driven diffusion strategy,the more sensitive the movement is to the environment,the better its survival.