基于同伦方法的高维非自治非线性系统动力学研究

项目名称： 基于同伦方法的高维非自治非线性系统动力学研究

项目编号： No.11202189

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 钱有华

作者单位： 浙江师范大学

项目金额： 25万元

中文摘要： 大部分实际工程问题都可用高维非自治非线性系统来描述，它的复杂动力学、分叉和混沌动力学研究是目前国际上非线性动力学领域的前沿课题，受到相关人员的广泛关注。由于利用高维系统可以更为准确地模拟工程问题，因此研究这类系统的复杂动力学行为具有重要的理论意义和工程实用价值。本项目拟通过理论分析和同伦数值计算相结合的方法研究高维非自治非线性系统的动力学，希望能够对实际工程问题中这类系统的设计和振动控制有一定的指导意义，主要内容将围绕高维非自治非线性动力学系统同伦方法理论、分叉和混沌动力学理论以及大幅振动系统的动力学进行研究，促进非线性动力学理论在实际工程中的应用。

中文关键词： 同伦分析方法；非自治系统；非线性动力学；；

英文摘要： Most of practical engineering problems are governed by high-dimensional non-autonomous nonlinear systems. The significance of such physical systems is mainly due to its complicated dynamical properties, bifurcations and chaotic motions. The intensive research subjects are thus at the forefront of nonlinear dynamics. In reality, the formalutation of high-dimensional systems can be used to describe realistic engineering problems mathematically. The in-depth understanding of these systems can enhance our availability in the design practice of engineering problems. In this project, we will improve and generalize the homotopy method to solve high-dimensional non-autonomous nonlinear systems. The obtained analytical solutions will be verified by using well-known numerical techniques. Furthermore, the theory of homotopy method, bifutcations and chaos dynamics,as well as large-amplitude vibration behaviour for high-dimensional non-autonomous nonlinear systems will also be investigated. It is expected that the present research will develop a novel and robust approach in solving practical problems in real-world engineering environments.

英文关键词： Homotopy analysis method；Non-autonomous systems；Nonlinear dynamics；；