双捕食者与双食饵的随机捕食系统动力学
Dynamic of Stochastic Predator-Prey Sys-tem with Two Predators and Two Prey
摘要: 本文研究了一类具有两个捕食者和两个食饵的随机捕食食饵模型，证明了系统具有唯一的全局正解，并利用随机李雅普诺夫函数给出了系统具有平稳分布的充分条件。最后分别在食饵种群存活和捕食者种群灭绝，及所有食饵和捕食者种群均灭绝这两种情况下，给出了捕食者种群均灭绝的充分条件。
Abstract: The paper studies a stochastic predator-prey model with two predators and two prey. Firstly, we prove that the system has a unique global positive solution. Then, by using the stochastic Lyapunov function method, we obtain sufficient criteria for the existence of stationary distribution and ergodicity. Finally, sufficient conditions for extinction of the predator population in two cases are shown, those are, the prey population survival and the predator population extinction, and all the prey and predator populations extinction.
文章引用：王欣琦, 张天四. 双捕食者与双食饵的随机捕食系统动力学[J]. 运筹与模糊学, 2023, 13(2): 666-680. https://doi.org/10.12677/ORF.2023.132069

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