几类随机种群模型的几乎必然持久性研究

Permanence of an ecosystem perturbed by environmental noises is an important definition that stands for coexistence of species, and also an important basis used to analyze its qualitative behaviors. Therefore the investigation of permanence of stochastic population models has an important theoretical and practical significance. Using new methods, the project aims to consider two types of almost sure permanence of population systems perturbed by environmental noises (white noise、Markovian switching and Lévy jump). The content includes: (1) To study the almost sure permanence of each species of stochastic single、two species models by virtue of the properties of martingale and stochastic comparison theorem. (2) For stochstic two-species population models, the project aims to apply the thought of limit sets in stochastic case to analyze the almost sure permanence of total population system and the almost sure permanence of each species. (3) Numerical simulation of the above stochastic population models. The project expects to obtain the adequate conditions under which the stochastic models are almost surely permanent. The main results of the project not only rich the stochastic biomathematics theory, but also provide some theoretical foundations and suggestions to environment regulation and artificial control that protect the survival of species.

随机扰动下的生态系统的持久性是表示种群长期生存的重要概念，又是分析种群系统定性行为的重要基础，因此研究随机生态系统的持久性有重要的理论和现实意义。本项目拟采用新的思路研究受到随机干扰（白噪声、Markovian 开关和 Lévy 跳）的种群模型的两种几乎必然持久性。内容包括：（1）应用鞅性和随机比较原理等研究几类随机单、两种群模型的每个物种几乎必然持久性。（2）利用随机极限集的思想，探讨几类随机两种群模型的种群系统几乎必然持久性和每个物种的几乎必然持久性。（3）上述随机模型的数值模拟。本项目拟给出几类随机种群模型几乎必然持久的适当条件。本项目的研究既丰富随机生物数学理论，又为保护物种持续生存的环境调控和人工控制等实际问题提供理论指导和参考建议。

随机扰动下的生态系统的持久性是表示种群长期生存的重要概念，又是分析种群系统定性行为的重要基础，因此研究随机生态系统的持久性有重要的理论和现实意义。本项目采用新的思路研究受到随机干扰的种群模型的几乎必然持久性。本项目在执行期间共发表或接受 SCI 论文9篇，中文核心1篇，具体结果为：（1） 研究了一类随机单种群模型的平稳分布存在性、常返性和强持久性。（2）研究了几类随机捕食者-食模型、互惠模型和几类随机Lotka-Volterra模型的平稳分布存在性、渐近稳定性、有界性、持久性等。（3）对上述随机模型的给出了数值模拟。本项目给出了几类随机种群模型持久生存的适当条件。本项目的研究既丰富随机生物数学理论，又为保护物种持续生存的环境调控和人工控制等实际问题提供理论指导和参考建议。