Abstract This work studies the stationary distribution of stochastic Lotka–Volterra population dynamics in state-dependent random environments. We first use the stochastic comparison approach to handle the difficulty caused by the state-dependent regime-switching. Then the ergodic property and positive recurrence are investigated by the theory of M -matrix under small perturbation. The mean of the stationary distribution is also estimated. At last, the main results are illustrated by a numerical example.

中文翻译：

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状态相关随机环境中随机种群动态的平稳分布

摘要 这项工作研究了随机 Lotka-Volterra 种群动态在状态相关的随机环境中的平稳分布。我们首先使用随机比较方法来处理由状态相关的政权切换引起的困难。然后用M-矩阵理论研究了小扰动下的遍历性和正递归性。还估计了平稳分布的均值。最后，通过数值例子说明了主要结果。