带有交错扩散的种群模型的平衡态模式

本项目研究具有扩散、自扩散和交错扩散的种群模型的解的稳定性和平衡态模式，揭示扩散、自扩散和交错扩散对种群生存的影响。具体来说，我们将从如下两个方面进行研究：.(1).在Neumann边界条件下，研究同时含有扩散、自扩散和交错扩散的种群模型的常数平衡解的局部稳定性和全局稳定性，图灵模式的产生条件和消失的条件，非常数正平衡解的存在性及其稳定性。.(2).在Dirichlet边界或Robin边界条件下，研究同时含有扩散、自扩散和交错扩散的种群模型的共存解的存在性，共存解的稳定性以及在参数平面上刻画共存区域。

In this project, we consider the stability and stationary patterns of population models with diffusion,self-diffusion and cross-diffusion.The purpose of this project is to reveal the effects of diffusion, self-diffusion and cross-diffuion on the survival of populations. Specifically, we will investigate the following two aspects:.(1).When the model is under homogeneous Neumann boundary condigion, we will investigate the local and global stability of the constant solutions, the appearance and disappearance conditions of Turing patterns, and the exsitence and stability of the non-constant solutions..(2).When the model is under homogeneous Dirichlet or Robin boundary condition, we will investigate the existence and stability of the coexistence solutions and characterize the coexistence region in parameter plane.