一类含扩散时滞的Prey-Predator模型的周期解存在与稳定性

研究一类含扩散与时滞的Prey-Predator模型，利用上下解及比较原理，证明了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，且对任意的非负初值函数这对周期拟解够成的区间是此系统的一个吸引子．

Existence and Stability of Periodic Solution of Prey- Predator Model with Diffusion and Time- Delays

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