一类随机时滞捕食者-食饵模型的动力学行为(英文)

Dynamics of a Delayed Predator-Prey Model with Stochastic Perturbation

研究了一类含时滞的Harrison型捕食者-食饵模型在随机扰动环境下的动力学行为.对于非时滞和时滞模型分别给出了局部和全局稳定性条件.通过白噪声分别对食饵人口增长率的和捕食者人口死亡率进行随机扰动,构建相应的随机时滞微分方程模型讨论环境噪声对其作用的动力学行为.在一定条件下,随机时滞模型存在随机最终有界的唯一全局正解且解的二阶均值是有界的.最后通过数值模拟对给出的分析结果进行了验证.

In this paper,we investigate a Harrison-type predator-prey model involving discrete time delay within fluctuating environment.We show the local and global stabilities of the non-delayed and delayed model.By perturbing growth rate of prey population and death rate of predator population with white noise terms,we construct the stochastic delay differential equation model to discuss the effect of environmental noise on the dynamical behavior.Under certain conditions,the stochastic model with time delay has a unique global positive solution which is stochastically ultimately bounded, and the average in time of the second moment of the solutions is bounded.Furthermore, we perform some numerical simulations to illustrate the analytical findings.