Based on the general mechanism of the interaction between Inner Mongolia grassland vegetation, grassland wind erosion and soil water erosion, a four-dimensional coupling high-dimensional nonlinear dynamic model of the interaction between wind erosion, water erosion, animal excrement and grassland vegetation in arid and semi-arid areas is established in the project for the grassland ecological characteristics of Inner Mongolia autonomous region. Through the theoretical analysis and numerical simulations of the differential dynamic system of the nonlinear dynamic model, the dynamic relationship between wind erosion process, water erosion process, herbivore excrement and vegetation growth is deeply studied, and the spatial distribution pattern and temporal evolution of wind erosion, water erosion, faeces and vegetation is simulated. The stability and other dynamic characteristics of the system are analyzed by nonlinear dynamics theory. The dynamic theory is verified by numerical simulation with the actual data of Inner Mongolia grassland vegetation ecosystem. It has important application value and practical significance to Inner Mongolia grassland ecological environment protection project.
本项目主要针对内蒙古自治区草原生态特性,基于内蒙古草原植被与牧区草地风力侵蚀和土壤水蚀相互作用的一般机制,建立干旱与半干旱地区风蚀、水蚀、动物粪便与草原植被相互影响的四维耦合高维非线性动力学模型。通过对非线性动力学模型的微分动力系统理论分析和数值模拟,将深入研究风蚀过程、水蚀过程、草食动物粪便和植被生长之间的动力学关系,模拟风蚀、水蚀、动物粪便及其植被的空间分布格局和时间演变的最终状态,用非线性动力学理论分析系统的稳定性等动力学特性。用内蒙古草原植被生态系统的实际数据进行数值模拟来进行动力学理论验证。本研究对内蒙古草原生态环境保护工程具有重要的应用价值和实践意义。
本项目研究了内蒙古草原植被生态系统的高维非线性动力学问题,项目组综合运用解析计算、理论分析和数值模拟等方法进行了系统的研究。项目的主要研究内容包括:建立了内蒙古草原植被生态高维非线性动力学模型,分析了内蒙古草原植被与环境因素相互作用的生态模型的非线性动力学特性,用内蒙古草原植被生态实际数据进行了非线性动力学数值模拟,改善植被与环境因素间的互相影响,提出控制生态系统非线性稳定性的有效方案,实现内蒙古草原水土保持、生态保护、防止荒漠化等工程实践提供有利的数据和理论参考。研究了一类改进的双时滞金融系统的Hopf分岔及动力学分析问题,求解了金融经济学中非线性时间分数阶偏微分方程的自适应多步分片插值再生核方法,通过生态经济系统建模与动力学分析可以为相关部门规范经济行为提供理论参考。