Dynamics of a  Predator-Prey Model with State-Dependent Maturation-Delay
报告人:刘胜强教授, 天津工业大学 2019年10月30日15:30-16:20
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.