项目名称: 个体尺度视角下种群调控问题的数学建模与研究
项目编号: No.11271104
项目类型: 面上项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 何泽荣
作者单位: 杭州电子科技大学
项目金额: 60万元
中文摘要: 本项目属于数学生态学范畴、种群控制理论与应用方向。基于个体尺度在生态学上的重要性,本项目首先建立若干考虑个体尺度分布、具有典型意义的种群控制模型(偏微分积分方程组或混杂系统)。其次研究系统的自然演化行为(如解的存在唯一性、非负性、有界性,系统的稳定性、持续性)和重要的控制问题(如种群状态关于基本参数的可控性、最优保护与最优收获),这些问题具有重要的生态学意义和很强的数学挑战性。通过研究,一方面揭示个体尺度的特殊作用,预测种群的演变趋势(如灭绝、持续生存),另一方面探讨种群资源保护与开发策略。研究过程将发展应用数学的理论和方法,推动学科进步,为维护生态平衡与生物多样性、科学管理可再生资源提供决策参考依据。项目预期成果不但具有学术理论价值,也具有广阔的应用前景。本项目也将为传染病的防控、经济系统调控、某些社会问题(如犯罪)等由非均质性对象构成的复杂系统的研究提供思想方法方面的支撑。
中文关键词: 个体尺度;生物种群;数学模型;行为分析;控制问题
英文摘要: This project belongs to mathematical ecology: population control theory and applications. Based on eological significance of body size, we firstly formulate some typical size-structured population control models, which are integral PDEs or hybrid systems. Then we investigate their evolutional behaviors (e.g. existence, nonnegativity and boundedness of a unique solution, stability and persistence of the syetms) and important control problems (e.g. controllability of population state via vital parameters, optimal harvesting or birth control). The problems above are ecologically valuable and mathematically challengable. The research process will reveal the special role of body size, forcast the evolutional trends of the populations (e.g. extinction or permenant persistence)on the one hand, and explore the reservation and exploitation strategies of population resources on the other hand. Furthermore the project can be expected to develop some beneficial methods, promote the subject, maintain ecological balance and bio-diversity, and supply scientific criteria for decision-making of renewable resources. The research results of the project are of theoretical importance and practical applicability, which will, in the mean time, support the study of complicated systems consist of heterogeneous objcects, such as the inte
英文关键词: Body size;Biological populations;Mathematical models;Behavioral analysis;Control problems