先锋－顶级种群反应扩散模型的平衡点线性稳定性

摘要

The linear stability of equilibria for a diffused pioneer and climax species competition model is dis-cussed.This system has at least 4 and at most 6 equilibria with two possible positive equilibria, and thus the dy-namical behaviors are very rich.All the constant equilibria of the model are given in the second section, and then the linear stabilities of these equilibria are analyzed in the third section.The sufficient condition or sufficient and necessary condition of the stability for every equilibrium is given.The linearization method is used accompanied with the eigenvalue skill.At last, an example is given to illustrate the application of the results with numerical sim-ulation and conclusion discussion.%研究扩散的先锋－顶级种群竞争模型的平衡态线性稳定性。所讨论的系统有4～6个平衡点，其中最多有2个正平衡点，其动力学性态十分丰富。运用线性化方法和特征根分析技巧等，对系统可能的各个常数平衡点的线性稳定性进行分析并给出每个平衡点稳定的充分条件或充分必要条件，最后举例说明结论的应用并进行了数值模拟和讨论。