摘要
非线性动力系统的响应特性主要由其内在的全局结构所决定,开展全局特性分析可以刻画出系统的全局结构形貌,从而全面了解其多稳态吸引子及其吸引域的形态.目前,基于状态空间离散思想的胞映射方法已成为刻画非线性动力系统全局结构最有效的方法.首先,基于胞映射理论,引入并行重构算法对胞-胞映射和胞分类处理过程进行了改进优化,提高了全局特性分析过程中最耗时的数值积分效率.然后,结合计算机高动态内存和大规模并行运算技术,建立了一套胞-胞映射过程快速且分类准确的全局特性并行分析方法.最后,利用全局特性并行分析方法刻画出了二维Mathieu-Duffing振荡器和三维Lorenz非线性动力系统的全局结构,并且在三维Lorenz系统状态空间划分尺度为51×51×61以及并行胞单元数量分别为10和100的条件下,相比于经典胞映射方法的总运算时间分别减少了81%和83%,验证了所提出的非线性系统全局特性并行分析方法的准确性和可行性.
The response characteristic of a nonlinear dynamical system is primarily determined by its intrinsic global structure.Conducting global characteristic analysis can delineate the morphological features of the system's global structure,thereby providing a comprehensive understanding of the system's multiple stable attractors and the morphology of their basins of attraction.Currently,the cell mapping method,based on the idea of state space discretization,has become the most effective approach for characterizing the global structures of nonlinear dynamical systems.Firstly,a parallel-reconstruction algorithm rooted in cell-mapping theory is first introduced to refine the cell-to-cell mapping and cell-classification procedures,thereby markedly accelerating the numerical integration that dominates global analysis.Subsequently,by exploiting high-dynamic-range memory hierarchies and large-scale parallel computing,a computationally efficient yet rigorously accurate parallel global-analysis method for cell-mapping processes is established.Finally,the proposed parallel global-analysis method is applied to delineate the global structure of a two-dimensional Mathieu-Duffing oscillator and a three-dimensional Lorenz system.Meanwhile,for the Lorenz system discretized into a 51×51×61 state-space grid,the total execution time is reduced by 81%and 83%relative to classical cell-mapping when 10 and 100 parallel cell units are employed,respectively,which verifies the accuracy and feasibility of the proposed parallel global-analysis method for nonlinear systems.
作者
马召召
余永华
周瑞平
杨庆超
柴凯
Ma Zhaozhao;Yu Yonghua;Zhou Ruiping;Yang Qingchao;Chai Kai(School of Naval Architecture,Ocean and Energy Power Engineering,Wuhan University of Technology,Wuhan 430063,China;School of Naval Architecture and Ocean Engineering,Naval University of Engineering,Wuhan 430033,China)
出处
《力学学报》
北大核心
2025年第10期2457-2465,共9页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(51839005,52201389)
国家重点研发计划(2023YFB2503905)
中国博士后科学基金(2024M762518)
中央高校基本科研业务费专项资金(104972025RSCbs0161)资助.
关键词
非线性动力系统
全局结构
胞映射方法
全局分析
nonlinear dynamical systems
global structure
cell mapping method
global analysis
