The effect of duffusion and spatial heterogeneity in the predator-prey system

• 1、Mathematics School,Hunan University,Changsha 410000
• 2、School of Mathematics and Physics,China University Of Geosciences,Wuhan 430074

Abstract：In the development of biomathematics, the study of dynamic analysis of biological population models has become an important research direction. In the latest research, many scholars pay attention to two important factors: the diffusion phenomenon of biological population and the heterogeneity caused by spatial environment, and study the effscts of these two factors on the behavior of species dynamics. Diffusive predator-prey model is very important in the practical application of biological population dynamics behavior. Based on the specific biological model as the theoretical background, by virtue of the comparison principle, linearization principle, combined with the related properties of linear logistic diffusion equation, the generalized response function Leslie Gower predator-prey model is studied systematically in this paper.We mainly study the Leslie Gower predator-prey model with diffusion phenomenon and spatial heterogeneous environment in this paper, further optimize the response function, and obtain the related properties of the solution of the model, such as boundedness and global existence. By using the linear diffusion equation to analyze the positive and negative of the principal eigenvalues, the stability of the semi trivial steady-state solution is obtained.

Keywords： Reaction-diffusion steady state solution linear diffusion equation comparison principle spatial heterogeneity stability.