一类具有扩散项的消费者-资源模型的稳定性分析

Stability analysis of a consumer-resource model with diffusion

研究了一类具有扩散项的消费者-资源模型.通过研究该模型的特征方程,得到了正平衡点局部稳定的条件和Hopf分支存在的条件.其次证明了系统的空间齐次/非齐次周期解的存在性,并给出了确定分支方向和分支周期解稳定性的条件.最后给出数值算例来验证所得结论.

We consider a consumer-resource model with diffusion term in this paper.Firstly,we obtain the conditions for the local stability of the positive equilibrium and the existence of Hopf bifurcation by studying the characteristic equation of the model.Secondly,we prove the existence of spatial homogeneous/nonhomogeneous periodic solutions,and give the conditions for determining the bifurcation direction and the stability of the bifurcation periodic solutions.Finally,a numerical example is given to verify our conclusion.