贵州喀斯特地区非光滑生物动力学模型与控制研究

Guizhou Karst region is famous frangible ecotope, the sustain of regional development is bad. By the influence of the geology and geomorphology,the climate,the hydrology and human unreasonable activities and so on, the stabilization, the anti-interference and the recovery capability are poor.If the artificial control is not carried out,it will make against the survival of humanity and living things. According to the current situation and the characteristics of Guizhou Karst regional environment and biological survivals ,this project aims to establish non-smooth biological dynamical models of Guizhou Karst regions. Employing the theories of differential equations,impulsive differential equations,impulsive delayed differential equations and non-smooth dynamical systems, we intend to obtain the controlling thresholds or the ranges of controlling thresholds of system stabilization of Guizhou Karst ecotope. Some dynamical behaviors of these system will be discovered or verified by Computer simulation technology. The results will promote the applied basic research of biodiversity protection and biological resources management of Guizhou Karst regions. The theory basis of sustained development and optimum development are provided for Guizhou regional economy and society.

：贵州喀斯特地区是著名的脆弱生态区，区域发展可持续性差，受地质地貌、气候、水文等生态因子的影响和人类不合理的开发利用等人为因素的影响，生态系统稳定性差，抗干扰能力差，自身恢复能力差。如果不加以人工控制，容易朝不利于人类与生物生存的方向发展。本项目拟根据贵州喀斯特地区环境及生物生存的现状与特点，利用数学生态学建模的方法，建立贵州喀斯特地区非光滑生物动力学模型。利用微分方程理论、脉冲微分方程理论、脉冲时滞微分方程理论与非光滑动力系统理论，得到贵州喀斯特地区生态系统稳定的控制阈值或控制阈值的取值范围。利用计算机仿真技术，发现或验证所研究系统的一些动力学行为。促进贵州喀斯特地区生物多样性保护与生物资源管理的应用基础研究，为该区域经济社会的可持续性发展与良性发展提供科学的理论依据。

根据贵州喀斯特地区生物系统的实际，建立.（1）.非光滑（阶段结构）单种群动力学模型,.（2）.非光滑（阶段结构）捕食（竞争）动力学模型,.（3）. 非光滑生态-传染病动力学模型,.利用微分方程理论、脉冲微分方程理论、脉冲时滞微分方程理论研究得到了贵州喀斯特地区非光滑生物动力系统控制的阈值或者其控制阈值的取值范围，结论为贵州喀斯特地区生物资源管理与生物多样性保护提供理论决策支撑。