一类具Allee效应的离散Lesile-Gower捕食被捕食模型的稳定性

Stabilityanalysis of a discrete Lesile-Gower predator-preymodel with Allee effect

目的研究一类离散的Lesile-Gower捕食被捕食模型的稳定性。方法通过应用雅可比矩阵讨论了系统平衡点的局部稳定性。结果在不含Allee效应和含Allee效应的情况下,分别得到了系统平衡点的局部稳定性的充要条件,并通过数值模拟验证了该条件的正确性。结论结果表明Allee效应对系统的稳定性具有加强作用。

Purposes- To study the stability of the discrete Leslie-Gower predator-prey model. Methods- The Jacobian matrix analysis method is used to investigate the local stability of the equilibrium points to the system. Result- In the conditions with and without Allee effect,the necessary and sufficient conditions of the local stability of equilibrium points to the system are obtained respectively.Furthermore,the validity of the conditions is verified via numerical simulations.Conclusion- The results show that the Allee effect can enhance the stability of the system.