一类含扩散与时滞的Prey-Predator模型的周期解

Periodic solution of Prey-predator model with diffusion and time-delays

利用上下解方法以及比较原理研究了一类含扩散与时滞的Prey-Predator模型,证明在一定条件下该模型的零平衡态及半平凡周期解的全局稳定性,并获得了这个系统具有一对周期拟解的充分条件.对任意的非负初值函数,这一对周期拟解构成的区间是此系统的一个吸引子.

In this paper, the Prey - predator model with diffusion and time - delay was investigated by using the method of upper and lower solutions and comparison principle. It proved that under some appropriate conditions the trivial solution and semi - trivial periodic solution of the models are globally asymptotically stable, the systems have a pair of periodic quasi - solutions and the sector between the quasi - solutions is an attractor of the models with respect to every nonnegative initial function.