脉冲反应扩散系统的最小临界域

Minimal Critical Domain of Impulsive Reaction-Diffusion Models

在假设生物种群具有脉冲出生阶段(由Beverton-Holt函数或Ricker函数描述)和连续的扩散阶段前提下,利用脉冲反应扩散系统讨论了有界区域下生物种群的持续生存.得到了种群持续生存的阈值(最小临界域),当有界区域长度大于此阈值时,生物种群可持续生存;当区域长度小于阈值时,生物种群灭绝.最后,对系统进行了数值模拟,数值结果表明,通过控制介质流动速度可实现生物种群在固定区域上的持续生存.

The impulsive reaction-diffusion models were proposed to study the persistence of species with reproductive stage and dispersal stage in bounded domains. It was assumed that,in reproductive stage,the impulsive growth was chosen to be Beverton-Holt function and Ricker function. The threshold（ also called the minimal critical domain）was got. The species could go extinct below the minimal critical domain,and could persist above the minimal critical domain. Finally,the numerical simulation of the system was carried out with the drift speed. The numerical results showed the drift speed can determine the persistence of the species in a bounded domain.