受扰动的捕食者–被捕食者模型的随机分岔分析
Stochastic Bifurcation Analysis of a Predator-Prey Model with Perturbations
摘要: 本研究针对一类具有随机增长率的捕食者–被捕食者系统，深入探讨了两种捕食者竞争单一被捕食者资源的动态行为及其随机演化规律。通过在不变曲面集上进行多阶段合理变形，推导出Fokker-Plank方程的封闭形式稳态解。在确立系统持久性的前提下，创新性地以环境噪声强度为分岔控制参数，揭示了所有种群的现象学分岔特性。本研究建立的随机分岔判据与竞争量化模型，为生物多样性保护与入侵物种控制策略的优化设计提供了动力学依据。
Abstract: In this paper, we focused on a predator-prey system with a random growth rate and deeply explored the dynamic behavior and stochastic evolution of two types of predators competing for a single prey resource. By performing multi-stage reasonable deformation on the invariant surface set, the closed-form steady-state solution of the Fokker-Plank equation is derived. Under the premise of establishing the persistence of the system, the environmental noise intensity was innovatively used as the bifurcation control parameter to reveal the phenomenological bifurcation characteristics of all populations. The stochastic bifurcation criterion and competition quantitative model established in this study provide a dynamic basis for the optimal design of biodiversity conservation and invasive species control strategies.
文章引用：崔一凡. 受扰动的捕食者–被捕食者模型的随机分岔分析[J]. 应用数学进展, 2025, 14(5): 417-433. https://doi.org/10.12677/aam.2025.145272

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