Some advances on global analysis of nonlinear systems
Some advances on global analysis of nonlinear systems
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DOI：
10.1016/j.chaos.2007.06.086
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发表时间：
2009-02
影响因子：
7.8
通讯作者：
Jianxue Xu
中科院分区：
文献类型：
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作者：
Jianxue Xu
非线性动力学中的全局分析是指对吸引子及其吸引域的研究;同时也涉及到了许多复杂的动力学行为和新现象，如分形盆边界、Wada盆边界、混沌吸引子中的无限不稳定周期轨道、混沌鞍和瞬态混沌、危机、吸引子的千疮百孔的盆、随机全局动力学等。用解析方法分析全球动力学是困难而有趣的，但成果却很少。因此，全球动力学的数值分析通常是主要的方法。全球分析抓住了各个领域更广泛社区的兴趣和想象力，如数学，物理学，气象学，生命科学，计算科学，工程学，医学等。重点介绍了中国在全球动力学领域的发展。
Global analysis in nonlinear dynamics means the study of attractors and their basins of attraction; meanwhile a lot of complex dynamical behaviors and new phenomena are concerned such as fractal basin boundary, Wada basin boundary, infinite unstable periodic orbits embedded in chaotic attractor, chaotic saddle and transient chaos, crises, riddled basin of attractor, stochastic global dynamics, etc. To analyze the global dynamics analytically is difficult and interesting while the results are few. Then, the numerical analysis for global dynamics is usually the main approach. Global analysis captures both the interest and imagination of the wider communities in various fields, such as mathematics, physics, meteorology, life science, computational science, engineering, medicine, and others. Emphasis is put mainly on the development in this global dynamics field in China.