报告地点：行健楼665
邀请人：万辉副教授
摘要：
In this talk, a stage structured predator-prey model of general nonlinear type of function response is established and analyzed. The state-dependent time delay (hereafter SDTD) is the time taken from predator's birth to its maturity, formatted as a monotonically increasing continuously differentiable bounded function on the number of mature predator. The model is quite different from many previous models with SDTD in the sense that the derivative of delay on the time is included in the model. First, for a large class of commonly used types of functional responses, including Holling types I, II and III, Beddington-DeAngelis-type (hereafter BD-type), etc, it is shown that the predator coexists with prey permanently if and only if the predator's net reproduction number is larger than one unit. Secondly, the local stability of equilibria of the model are also discussed. Finally, for the special case of BD-type functional response, it is shown that if the system is permanent, that the derivative of SDTD on the state is small enough and that the predator interference is large enough, then the coexistence equilibrium is globally asymptotically stable.