一类随机非光滑振动系统相空间中不同吸引域边界的随机分形  

RANDOM FRACTAL BOUNDARIES OF DIFFERENT ATTRACTING DOMAINS IN THE PHASE SPACE OF A STOCHASTIC NON-SMOOTH OSCILLATORY SYSTEM

作　　者：雷华[1] 甘春标[1] 谢潮涌[1] 

机构地区：[1]浙江大学航空航天学院应用力学研究所,杭州310027

出　　处：《工程力学》2010年第3期1-5,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(10672140)

摘　　要：由于复杂动力学行为而导致非线性振动系统相空间中不同吸引子的吸引域边界出现分形的情况比较普遍。该文数值研究一类受周期与有界噪声激励联合作用的碰振系统的全局动力学特征。通过改进胞映射方法,并给出庞卡莱映射的一种特殊形式,以对此类系统的全局动力学行为进行了模拟。结果表明:通过调整参数值,系统相空间里也可出现多个随机吸引子,不同吸引域的边界将呈现随机分形形状。It is common for many oscillatory systems to encounter incursive fractal boundaries between different attracting domains in their phase spaces due to their complex dynamical behaviors.This study is focused on the global dynamics of a nonlinear oscillator with rigid constraints under multiple harmonic and bounded-noise excitations.The well-known cell mapping method is developed,and a specific Poincare map is then introduced to simulate the global dynamics of the system.It is shown that several kinds of stochastic attractors may coexist in the space of such system by adjusting the parameters’ values.In addition,random fractal boundaries will arise between different attracting domains of stochastic attractors.

关 键 词：非光滑振动 有界噪声 胞映射 随机吸引子 随机分形 

分 类 号：O324[理学—一般力学与力学基础] O175[理学—力学]