基于并行和细分的高效胞映射方法及应用研究

项目名称： 基于并行和细分的高效胞映射方法及应用研究

项目编号： No.11302170

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 岳晓乐

作者单位： 西北工业大学

项目金额： 25万元

中文摘要： 胞映射方法是研究随机动力系统响应和分岔问题的一种有效数值方法，尤其是多吸引子共存时的情况，但在分析多自由度随机动力系统的响应和分岔问题时耗时太长，因此非常有必要发展一种即快速又准确的胞映射方法。本项目基于并行算法，围绕一步转移概率矩阵创建、图分析算法和矩阵分析算法三个过程，探讨胞映射方法的快速计算问题。基于复合胞坐标系概念，提出一种细分方法进一步提高胞映射方法的准确性。针对两类典型的非高斯噪声激励模型：有界噪声和泊松白噪声，研究多吸引子共存时随机动力系统的响应和分岔问题，并将研究结果推广到多自由度的情形，揭示不同随机分岔定义之间的内在联系，阐明随机响应与确定性动力系统不稳定流形之间的关系。本项目的完成将扩大胞映射方法的应用范围，为多吸引子共存时多自由度系统的随机响应和随机分岔问题研究提供有力工具，丰富随机动力学的研究成果。

中文关键词： 胞映射方法；全局动力学；不变流形；非高斯噪声；响应和分岔

英文摘要： The cell mapping method is an efficient numerical method to research the response and bifurcation of stochastic dynamical systems, especially the situation that multiple attractors coexist. However, it is time-consuming in analyzing the response and bifurcation of multi-degree of freedom dynamical system. Hence, it is very necessary to develop a fast and accurate cell mapping method. Based on the parallel algorithm, this project centers around three processes of the creation of one-step transition probability matrix, digragh analysis algorithm and matrix analysis algorithm, to explore the rapid calculation of cell mapping method. Based on the conception of composite cell coordinate system, this project proposes a subdivision method to further increase the accuracy of cell mapping method. For two typical models of non-Gaussian noise excitation: bounded noise and Poisson white noise, this project studies the response and bifurcation of stochastic dynamical system with multiple attractors and extends the results to multi-degree of freedom dynamical system, in order to reveal the intrinsic connection of different definitions of stochastic bifurcation and clarify the relationship between stochastic response and unstable manifold of deterministic dynamical system. The fulfillment of this project can expand the applica

英文关键词： cell mapping method；global dynamics；invariant manifold；non-Gaussian noise；response and bifurcation