基于比率依赖的Leslie捕食扩散模型的Turing不稳定性

Turing instability in a ratio-dependent Leslie predator-prey model with diffusion

针对一类带有比率依赖的HollingⅡ型功能反应的Leslie捕食模型的扩散问题进行研究.首先得到无扩散时正平衡点的稳定条件,讨论在正平衡点附近Hopf分支的存在性和稳定性;其次,讨论了扩散存在时对正平衡点稳定性产生的影响;最后给出数值模拟验证.

Diffusion problem of Leslie predator-prey model with ratio-dependent Holling type II functional response was studied. First, when diffusion was absent, the authors obtained stability condition of positive equilibrium. Furthermore, they researched the existence and stability of Hopf bifurcation near the positive equilibrium. Then, the effect on stability of positive equilibrium was investigated when diffusion was present. Finally, for explaining our result, numerical simulations were given.