一类n-种群捕食–竞争随机系统持久性研究

Research on Persistence of a Class of n-Species Predator-Competition Stochastic System

摘要: 本文研究一类n种群捕食–竞争随机系统的几乎必然持久性。通过构造适当的Liapunov函数，运用Itô公式得到该系统全局唯一正解的存在性和最终随机有界性，利用非负半鞅收敛理论得到该随机系统的持久性充分条件，并将该持久性充分条件拓展到该随机非线性系统，并得到该随机非线性系统满足特定的条件依概率1灭绝。最后，通过数值模拟验证我们所得结论的正确性。

Abstract: This paper studies the almost inevitable persistence of a class of N-population predator-competitive stochastic systems. By constructing an appropriate Liapunov function and applying the Itô formula, the existence of the globally unique positive solution and the ultimate random boundedness of the system are obtained. The sufficient condition for the persistence of the random system is obtained by using the non-negative half-martingales convergence theory, and this sufficient condition for persistence is extended to the random nonlinear system. And it is obtained that the stochastic nonlinear system satisfies specific conditions and becomes extinct with a probability of 1. Finally, the correctness of the conclusion we reached was verified through numerical simulation.