参数依赖吸引子逼近的面向集合的路径跟踪方法
A set-oriented path following method for the approximation of parameter dependent attractors
摘要：
本文提出了一种面向集合的路径跟踪方法来计算参数依赖动力系统的相对全局吸引子。我们开始与一个固定的参数$λ_0$由面向集合的细分方法计算的相对全局吸引子的初始近似。通过使用先前获得的近似的参数依赖的相对全局吸引子，我们可以跟踪它相对于一个一维参数$λ> λ_0$，而无需重新启动整个细分过程。我们说明了面向集合的路径跟踪方法的可行性，通过探索模型中的剪切流在过渡到湍流的动力学。
英文摘要：
In this work we present a set-oriented path following method for the computation of relative global attractors of parameter-dependent dynamical systems. We start with an initial approximation of the relative global attractor for a fixed parameter $λ_0$ computed by a set-oriented subdivision method. By using previously obtained approximations of the parameter-dependent relative global attractor we can track it with respect to a one-dimensional parameter $λ> λ_0$ without restarting the whole subdivision procedure. We illustrate the feasibility of the set-oriented path following method by exploring the dynamics in models for shear flows during the transition to turbulence.
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