一类具有双平方根响应函数的状态依赖反馈控制模型

A Predator-prey State Dependent Feedback Control Model with Double Square Root Response Function

基于微分方程几何理论和非线性动力系统理论,针对"羊群行为"构建一类具有双平方根响应函数的状态依赖反馈控制模型,特别研究了忽略捕食者在捕食过程中的平均耗时因素情形下系统的动力学行为,利用后继函数法分析了阶一周期解的存在性,得到了阶一周期解存在的充分条件,并通过数值模拟进行了验证。

Based on the differential equation geometry theory and nonlinear dynamical system theory,a state-dependent feedback control model of predator-prey with double square root response function is constructed for"herd behavior".The dynamic behavior of the system is studied especially when the average time-consuming factor of predator is neglected.The existence of the order-1 periodic solution is analyzed by using the successor function method.Sufficient conditions for the existence of order-1 periodic solutions are obtained and verified by numerical simulation.