广义随机经济生物系统的建模与控制

In this research plan, the study of modeling and control for descriptor stochastic economic biological systems is proposed. Considering impact of economic interest to stochastic biological systems, the descriptor stochastic economic biological system model is established. Here the study of stochastic algebraic equation parts of the system model is emphasized for better understanding of its meaning of economics and biology. The referenced modeling methods for the systems are developed. Then ways to investigate system structures and properties are founded, including the existence and uniqueness of the system solutions, stability and controllability, as well as bifurcation and chaos etc. Especially, the structures and properties of some typical descriptor stochastic economic biological system model are investigated in details. The controller design and control police as well as simulation technique, are provided to make the system model work well. This project will provide a new way to study the descriptor stochastic economic biological systems. For the systems with random and stochastic characteristics, the impulse behavior is discussed to show its influence to the systems. It also will provide analysis method and control police for further study of these kinds of systems, to complete and develop stochastic control theory, and broaden its application fields.

研究广义随机经济生物系统的建模与控制问题。考虑经济利益对随机生物系统的影响，建立广义随机经济生物系统模型，侧重研究系统模型中随机代数方程部分以及其在经济学和生物学中的含义，给出有参考借鉴价值的系统建模方法。在此基础上，探讨系统结构分析手法，研究系统的结构性质与复杂性，包括系统模型解的存在性、惟一性、稳定性和能控性，以及系统的分岔与混沌现象等，具体给出典型的广义随机经济生物系统模型的基本性质和复杂性行为。运用先进的数学理论与控制手段，对广义随机经济生物系统提供有效的控制策略与控制器设计方案，以及计算机仿真技术。本项目的实施与完成，将开辟研究广义随机经济生物系统建模与控制的新途径。对于具有随机和统计特性的广义经济生物系统，阐述系统脉冲行为及其对系统的影响。为进一步研究广义随机经济生物系统提供相关的分析方法和控制策略，完善和发展广义随机系统理论，拓宽其应用研究领域。

本项目利用广义随机系统理论，提出了一种系统的生物模型的建模、分析与控制方法。考虑生物模型都会受到某种因素的限制，如“纯利润等于总收入减去总成本”的经济学原理或传染病模型中总人口数不变的性质，给出了一系列实用的广义随机经济生物系统的建模方法及案例；在此基础上，利用微分方程定性理论和随机过程理论，确立了典型的广义随机经济生物系统结构性质和复杂性行为的分析方法，如正平衡点附近的随机稳定性、Hopf分岔，奇异诱导分岔等；借助于正系统理论，提出了分析广义随机经济生物系统正性和稳定性的若干判定方法；对带有布朗运动的广义随机系统、Markov跳变广义系统进行了系统地分析与设计，取得了若干研究成果，为分析与控制广义随机经济生物系统提供了有力的理论支撑。开展了广义随机经济生物系统在实际中的应用研究，以近海渔业，沿海湿地保护和食饵捕食生态系统为背景，为保护和合理开发生态资源提供了一种有效可行的方法。为进一步研究广义随机经济生物系统建模、分析与控制开辟了新途径。