PMUCR方法在高维非线性动力学系统中的应用

对现有的若干种胞映射方法应用于高维非线性动力学系统全局分析时存在的局限性进行了分析,在此基础上,提出了胞映射方法应用于高维系统时需遵循的几个原则:选择合适的分析平面;减少数据量;确定吸引子在相空间中的位置。根据这些原则,对胞参考点映射法(PMUCR)进行了改进,并对该改进方法应用于2维系统和4维系统时消耗的相对CPU时间进行了比较,结果表明,该改进方法能有效地应用于高维非线性动力学系统中。最后以船舶机械非线性隔振系统为例,分别分析了该改进方法在系统呈现周期运动和混沌运动时的应用。

PMUCR Method with Applications to High-dimensional Nonlinear System

Analysing the inefficiency of the conventional Cell Mapping Methods in the global analysis for high-dimensional nonlinear system,several necessary principles applied to high-dimensional systems are proposed: the appropriate selection of the investigating plane,the reduction of the data size, the determination of the coordinates of attractors in the phase space.Thus the idea of dynamic array is introduced into the method of Point Mapping Under Cell Reference(PMUCR) to improve the computing efficiency.A comparison of the CPU for 2D system and 4D one is carried out,and the results confirm the efficiency of this modified method for high-dimensional system.Finally,the periodic and chaotic motions of a nonlinear vibration-isolation system for on-board machinery are investigated.