污染环境中随机生物种群模型的动力学研究

项目名称： 污染环境中随机生物种群模型的动力学研究

项目编号： No.11301207

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 刘蒙

作者单位： 淮阴师范学院

项目金额： 23万元

中文摘要： 环境污染是当今世界各国的严重问题，研究污染环境中生物的生长规律对治理污染具有重要的理论和实际意义。本项目拟建立若干污染环境中受到随机干扰（包括白噪声、Markovian开关和Lévy跳）的种群模型，并研究其若干动力学性质，包括：（1）拟利用随机分析理论、Lyapunov第二方法、M矩阵和图论，得到相应模型中每个物种生存和灭绝的阈值。（2）拟利用随机分析理论、Lyapunov第二方法和图论研究模型的持久性。（3）由于经典的"平均条件"思想是研究确定性生物种群模型解的全局吸引性的强有力工具，本项目拟把该思想推广到随机的情形，并用其给出污染环境中随机生物种群模型解的全局吸引性的充分条件。本项目期望，通过这些研究揭示出不同类型的随机干扰对污染环境中生物种群模型的生存和灭绝阈值、持久性和全局吸引性的影响，进一步为一些实际问题的解决，例如，如何更好地保护环境和治理污染，提供一些理论依据和建设性意见。

中文关键词： 随机干扰；种群模型；环境污染；；

英文摘要： In the present world, environment pollution is a serious problem for all countries, the investigation of growth law of creatures in a polluted environment is of important theoretical and practical significances to control pollution. This project will formulate some population models with random perturbations (including the white noise, Markovian switching and Lévy jumps) in a polluted environment, and will investigate some dynamical properties of these models, including: (1) To obtain the threshold between persistence and extinction for each population in corresponding models by using the theory of stochastic analysis, Lyapunov's second method, M matrix and graph theory. (2) To study the permanence of models by using the theory of stochastic analysis, Lyapunov's second method and graph theory. (3) Because the classical "average conditions" thought is a powerful tool for investigating the global attractivity of solutions to the deterministic population systems, this project shall generalize this thought to the stochastic case, and shall use it to give the sufficient conditions for the global attractivity of solutions to the stochastic population models in a polluted environment. By investigating these problems, this project expects to reveal the impacts of different stochastic perturbations on the persistence-an

英文关键词： stochastic pertubations；population models；environmental pollution；；