一个带有交叉扩散的捕食-被捕食模型的动力学性质

Dynamics of a Predator-prey Model with Cross Diffusion

对一个带有自扩散和交叉扩散的捕食-被捕食模型进行研究,分析了该模型平衡点的局部以及全局稳定性,研究了当系统同时考虑自扩散和交叉扩散影响时稳定性的变化。证明了交叉扩散系数的变化对于该模型的局部和全局稳定性有重要的影响,并且证明了由交叉扩散导致的图灵失稳的多种情形。

In this paper,apredator-prey model with self-diffusion and cross-diffusion is studied.The local and global stability of the system＇s equilibrium are studied,and the effects of self-diffusion and cross-diffusion on the stability are analyzed.The analysis shows that the cross-diffusion can play an important role in the local and global stability of the system.Furthermore,we found that the cross diffusion can cause the Turing instability in a variety of situations.