用蒙特卡罗方法研究混沌的有序性
Exploration of Order in Chaos with Replica Exchange Monte Carlo
摘要：
介绍了一种探索非线性动力系统不稳定结构的方法。该方法基于随机交换蒙特卡罗（REM）对初始条件和参数的抽样，对稀有初始条件的搜索和稀有初始条件与参数的联合搜索都是有效的。这里讨论的例子包括混沌中不稳定周期轨道的采样和搜索不稳定不动点的稳定流形，以及构造映射的全局分支图。
英文摘要：
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of rare initial conditions and for the combined search of rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and search for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.
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