基于噪声影响的生物修复系统渐近行为及数值计算方法研究

环境污染物的生物修复过程涉及一个非常复杂的生化反应网络。其数学模型需要考虑环境噪声、变时滞、弥散和水的对流等因素的综合影响。鉴于目前国内外对生物修复理论的数学研究多局限于单个确定性因素，还没有从系统和随机的角度揭示生物修复过程中的动力学行为和反应机理。而且所采用的数值方法计算成本高。本项目以具有不确定参数和弥散对流随机生物修复系统模型为研究对象， 拟采用随机Razumikhin方法和LaSalle原理开展动力学行为的研究，利用多层Monte Carlo弱Galerkin方法讨论系统模型的数值解法。以生物修复过程的持久性为目标，利用随机分析和矩阵理论研究系统的稳定性、散逸性、数值解的指数稳定性，发展和探讨有效可操作的判断准则。本项目的特色和创新点是建立一个包含多因素的生物修复污染物的动力系统，并给出一个高效的稳定性和散逸性的判断准则。为发展生物修复技术理论及促进其应用提供可靠的理论基础。

Bioremediation of environmental contaminant involves a sophisticated reactive network. Its mathematical modeling requires considering a larger number of components such as environmental noise, varied-time delay, dispersion, and convection. However, the current mathematical studies of environmental remediation are limited to individual and deterministic components, and have not investigated the dynamics and reactions of the bioremediation components from a system and stochastic prospective. In addition, the currently used methods for mathematical modeling is computationally expensive. This project is focused on the bioremediation in an advection-dispersion system with stochastic parameters. The dynamics of the system will be studied using the stochastic Razumikhin method and LaSalle theory. The multi-level Monte Carlo and weak Galerkin method will be used for obtaining numerical solutions. To achieve sustainability of bioremediation, we will use stochastic analysis and matrix theory to explore and to establish effective evaluation criteria for stability, dissipation, and the exponential stability of the numerical solutions. The novelty of this project is to develop mathematical equations of a dynamics system with multiple components of bioremediation and to provide effective evaluation criteria for stability and dissipation of the system. The mathematical results will provide a solid basis for further development of bioremediation methods and advancement of their practical applications.