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首页> 外文期刊>Advances in Difference Equations >Dynamical analysis of a ratio-dependent predatora??prey model with Holling III type functional response and nonlinear harvesting in a random environment
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Dynamical analysis of a ratio-dependent predatora??prey model with Holling III type functional response and nonlinear harvesting in a random environment

机译：随机环境下具有Holling III型功能反应和非线性收获的比率依赖型捕食者食饵模型的动力学分析

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摘要

The objective of this paper is to study the dynamics of the stochastic ratio-dependent predatora??prey model with Holling III type functional response and nonlinear harvesting. For the autonomous system, sufficient conditions for globally positive solution and stochastic permanence are established. Then, applying comparison theorem for stochastic differential equation, sufficient conditions for extinction and persistence in the mean are obtained. In addition, we prove that there exists a unique stationary distribution and it has ergodicity under certain parametric restrictions. For the periodic system, we obtain conditions for the existence of a nontrivial positive periodic solution. Finally, numerical simulations are carried out to substantiate the analytical results.
机译：本文的目的是研究具有Holling III型功能响应和非线性收获的随机比率依赖的捕食者-食饵模型的动力学。对于自治系统，为全局正解和随机持久性建立了充分的条件。然后，将比较定理应用于随机微分方程，获得了灭绝和均值持续存在的充分条件。此外，我们证明存在唯一的平稳分布，并且在某些参数限制下具有遍历性。对于周期系统，我们获得了一个非平凡的正周期解的存在条件。最后，进行数值模拟以证实分析结果。

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