随机参数作用下碰撞振动系统的非线性动力学研究

项目名称： 随机参数作用下碰撞振动系统的非线性动力学研究

项目编号： No.11202160

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： 王亮

作者单位： 西北工业大学

项目金额： 26万元

中文摘要： 非线性随机动力学的研究是当今学术界的一个热点问题。目前，关于随机系统的讨论大部分集中于光滑情形，涉及碰撞振动系统的研究相对较少，而现实中的很多动力系统同时兼有随机与碰撞的特性，因此，研究随机碰撞振动系统有利于人们更好地认识客观世界。本项目主要以随机参数作用下的碰撞振动系统为研究对象，对系统的各种动力学现象和混沌控制问题进行讨论，拟初步建立一套针对此类随机碰撞振动系统的理论分析方法和数值模拟方法。研究随机参数对碰撞振动系统分岔、混沌、吸引子、吸引域等动力学现象的作用机制；发展和设计一些面向随机碰撞振动系统的混沌控制方法，探讨确定性系统与随机系统混沌控制的异同以及随机参数对碰撞振动系统混沌控制的影响机理。本项目的进行将进一步丰富碰撞振动系统的研究成果，为其他类似系统的研究提供思路，对随机非线性系统的发展起到一定的推动作用。

中文关键词： 碰撞振动系统；随机参数；噪声；随机动力学；混沌控制

英文摘要： Nonlinear stochastic dynamics has become one of the most attention-grabbing research areas of current academic community. Up to now, the existing study on stochastic systems is mainly conducted for smooth systems, while there're few results obtained for vibro-impact systems. Yet, in practice, systems are usually characterized by both randomness and impact, so the investigation of stochastic vibro-impact systems act as an important tool to know about the objective world. This program aims at vibro-impact systems interacted with random parameter, various dynamic phenomena and chaos control of stochastic vibro-impact systems will be investigated. The theoretical method and the numerical simulation of studying the vibro-impact systems with random parameter will be tentatively established. The mechanism of action of random parameter on the dynamic phenomena like bifurcation, chaos, attractor and basin of attraction is discussed, and some methods of chaos control for stochastic vibro-impact systems are proposed. Furthermore, the similarities and differences between the chaos control of deterministic systems and stochastic systems are discussed, and the effect of the random parameter on the chaos control of impact systems is also studied. The fulfillment of this program can enrich the research achievements of the vibro

英文关键词： vibro-impact system；random parameter；noise；stochastic dynamics；chaos control