噪声影响下具有不确定因素的恒化器动力学模型研究

微生物生长和繁殖的过程涉及到一个非常复杂的生化反应网络，其中存在许多现实的不确定因素，同时还不可避免地会受到各种不可预知的随机噪声干扰。鉴于目前国内外对噪声影响下具有不确定因素的恒化器模型的研究还很少，而生物工作者所用的主要是统计学方法，不能很好地揭示微生物培养过程中内在的动力学机理以及随机噪声与不确定因素对其产生的动力学影响，本项目着重从动力学角度，以微生物发酵培养、废水生物处理等为实际背景进行建模和分析。主要研究内容包括：针对存在噪声干扰和不确定因素的微生物恒化培养过程，建立恰当的动力学模型，研究系统的持续性、稳定性以及微生物种群的多样性，探讨对系统进行有效控制的方法和途径；在此基础上，进一步研究在随机噪声和不确定因素影响下系统的渐近行为，并对其中存在的相关参数进行估计和假设检验，发展和探讨噪声影响下微生物恒化培养的最优化理论，为从事微生物发酵与应用研究的生物工作者提供可靠的数学依据。

The process of microbial growth and reproduction involves a very complex biochemical reaction network, in which there are many realistically uncertain factors, moreover, it may also be inevitably affected by a variety of unpredictable random noise interference. In view of the currently domestic and foreign researches on chemostat models with uncertainties under the influence of noise are still seldom, and the methods used by the biological researchers are mainly statistics, which can't well reveal the intrinsically kinetic mechanism and the kinetic effects of the random noise and uncertainties in the process of microbial cultivation. This project will proceed mainly from the kinetic modeling point of view, using microbial fermentation and biological treatment of wastewater etc. as the real background of research. Our main aims of this project are: In order to deal with the presence of noise and uncertainty factors in the process of microbial chemostat culture, we will develop appropriate kinetic models to study the persistence, stability of the system and the diversity of microbial communities, and explore the effective control methods/ways to the systems; On the basis of these, we will further study the asymptotic behavior of the systems under the influence of random noise and uncertainty factors, carry through the estimation and hypothesis testing to the related parameters, develop and explore the optimization theory of microbial chemostat culture under the influence of noise, and provide reliable mathematical basis to the biological researchers in the area of microbial fermentation and application.