一类带有脉冲的生物入侵随机模型的分析

Analysis of A Stochastic Biological Invasion Model with Impulses

自然界存在大量的捕食关系,生物入侵是一种特殊的捕食关系。考虑到现实中两种群的关系难免受到环境的白噪声干扰和人类或自然灾害的脉冲干扰,选择研究具有脉冲的随机模型更有实际意义。首先从问题出发逐渐引入并建立模型,然后构建一个无脉冲的等价模型来证明此模型正解的存在唯一性,接着给出两种群持久和灭绝的条件,最后用数值模拟将模型应用于生物入侵,验证理论的合理性。

Biological invasion is a special type of predation in nature.In fact, it is inevitable for the population relationship between predators and preys to be influenced by the interference of white noise in the environment and of the impulse of human activities or natural disasters. In this paper, we studied a stochastic predator-prey model with impulses. First, we introduced and established the model based on the problem. Second, we proved the existence and uniqueness of the positive solution by constructing an equivalent model without impulses. Third, we obtained the sufficient conditions for the permanence and extinction of the two populations. Finally, we applied this model to biological invasion through numerical simulations and verified its reasonability.