空间异性环境中Leslie-Gower捕食模型的稳定性与分支分析
Stability and Bifurcation Analysis of the Leslie-Gower Predator-Prey Model in Spatial Heterogeneity Environment
摘要:
本文考虑空间异性环境中修正的Leslie-Gower捕食模型。首先通过分析每个半平凡解相应特征值的符号，得到半平凡解的局部稳定性，其次利用局部分支理论证得分支解的存在性，最后经过讨论和证明，获得分支的方向以及分支解的稳定性。
Abstract:
We concerned about the modified Leslie-Gower predator model in a spatially heterogeneous environment. Firstly, the local stability of the semi-trivial solution is obtained by analyzing the sign of the principal eigenvalue corresponding to each semi-trivial solution. Secondly, the existence of bifurcation solutions is proved by using the local branch theory. Finally, the direction of the branch and the stability of its solution are obtained after the discussion and proof.
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