时滞三维顺环捕食系统的周期解和概周期解

Periodic and Almost Periodic Solutions of a Three-dimensional Prey-predator Cyclic Model with Multi Time-delays

关键词:  三维顺环捕食系统  时滞  Holling Ⅱ功能性反应  周期解  概周期解

Key words:  three-dimensional pre-predator cyclic model  time-delays  Holling Ⅱ functional response  periodic solusion  almost periodic solution

摘要:

讨论一类含多个时滞且具"基于比率"Holling Ⅱ功能性反应的三维顺环捕食被捕食系统.证明了系统的一致持久性;当系统是周期系统,通过构造Liapunov泛函,得到了系统存在唯一的全局吸引的正周期解的充分条件;当系统是概周期系统时,通过Razumikhin函数法,证明了系统存在唯一且一致渐近稳定的正概周期解.

Abstract:

A three-dimensional prey-predator cyclic system with ratio dependent Holling Ⅱ functional response and time-delays is discussed. By the Liapunov function method and Razumikhin function method,we proved the uniformly persistence of the system,the existence of a unique positive periodic solution which is globally attractive and a unique positive almost periodic solution which is uniformly asymptotically stable.