空间异性对Crowley-Martin型扩散的Leslie-Gower捕食模型的影响

The effect of spatial heterogeneity on a diffusive Leslie-Gower predator-prey model with Crowley-Martin type functional response

考虑空间异性环境中带有Crowley-Martin型功能反应函数的扩散的Leslie-Gower捕食模型.首先运用线性化分析的方法讨论半平凡解的稳定性,结果表明空间异性环境中扩散会改变食饵灭绝的半平凡解的稳定性;其次应用局部分支定理得到共存解的存在性,并对分支方向和分支解的稳定性进行了刻画.

We consider a diffusive Leslie-Gower predator-prey model with Crowley-Martin type functional response in the spatially heterogeneous environment.First,the stability of the semi-trivial solutions is discussed by using the method of linearization analysis.The results show that the stability of the semi-trivial solution for extinction of prey is changes as the diffusion rate varies in the spatially heterogeneous environment.Secondly,the existence of coexistence solution is obtained by using the local bifurcation theory,and the direction of bifurcation and the stability of the local bifurcation solution are discussed.