Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study.
Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study.
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预测无限维动力系统的混沌：Kuramoto-Sivashinsky 方程，案例研究。
DOI：
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发表时间：
1991
影响因子：
11.1
通讯作者：
D. Papageorgiou
中科院分区：
文献类型：
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作者：
Y. Smyrlis;D. Papageorgiou
广泛的计算结果准确地描述了Kuramoto-Sivashinsky方程的混沌过渡。特别是，我们遵循的振荡动力学在一个窗口，支持一个完整的序列的周期加倍分岔之前的混乱。多达13个周期的double以下，并用于计算的费根鲍姆数的级联，使一个精确的数值评估的非线性系统的普遍行为的理论，一个无限维的动力系统。此外，在混沌阈值的动力学表现出自相似的行为，证明并用于计算一个通用的缩放因子，这也是从非线性映射理论产生的，可以使连续的解决方案进入混沌状态。当系统进入混沌状态后，非周期解和周期解交替出现，并且存在一个被混沌区域分隔的周期为6的解。
The results of extensive computations are presented to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular we follow the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos. As many as 13 period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a self-similar behavior that is demonstrated and used to compute a universal scaling factor, which arises also from the theory of nonlinear maps and can enable continuation of the solution into a chaotic regime. Aperiodic solutions alternate with periodic ones after chaos sets in, and we show the existence of a period six solution separated by chaotic regions.