季节性对一类食饵-捕食者模型动力学稳定性的影响

Effect of Seasonality on the Dynamic Stability of a Prey-Predator Model

在经典的两种群食饵-捕食者模型中引入一个新的捕食者种群,新捕食者种群将捕食原系统中的食饵种群,并和原捕食者种群形成竞争。然后,采用食饵种群遵循Logistic增长和选取Crowley-Martin型功能性反应函数建立自治的三种群动力学模型。在该自治模型中对捕获率引入季节性变化的正弦周期函数,从而给出非自治的三种群动力学模型,分析推导了自治的三种群动力学模型的有界性,得到该模型的平衡点及其存在条件,利用雅可比矩阵和罗斯-霍维兹判据分析了平衡点的局部稳定性。数值模拟分析表明,对食饵-捕食者系统季节性因素而言,具有持久性和灭绝性,并且能够增强生态系统的稳定性。

In the classic two-species prey-predator model,a new predator species was introduced into the model.The new predator population captures the prey population in the original system and forms competition with the original predator popu-lation.Therefore,we established an autonomous three-population dynamics model by Logistic growth and Crowley-Martin type functional response function.Next,a sinusoidal periodic function of seasonal variation is introduced into this autonomous model,and a non-autonomous three-population dynamics model is given.Then,the bounded property of an autonomous three species dynamics model is derived.The equilibrium point and its existence conditions are obtained,and the local stability of the equilibrium point is analyzed by Jacobian matrix and Routh-Hurwitz criterion.In addition,the numerical simulation results show that seasonality is persistent and extinct to the predator-prey system,which can enhance the stability of the ecosystem.