广义Kuramoto-Sivashinsky方程的非线性预报
Nonlinear forecasting of the generalised Kuramoto-Sivashinsky equation
摘要：
我们研究的出现斑图形成和混沌动力学的一维（1D）广义Kuramoto-Sivashinsky（gKS）方程的时间序列分析，特别是非线性预测方法，这是基于混沌理论的概念和适当的统计方法。我们分析了两种类型的时间信号，一个本地的和一个全球的，发现在这两种情况下的gKS解决方案的动力学状态经历了从高维混沌的周期脉冲振荡，通过低维确定性混沌与系统的控制参数增加的过渡。我们的研究结果表明，建议的非线性预测方法可以阐明系统的动力学方面的可预测性。
英文摘要：
We study the emergence of pattern formation and chaotic dynamics in the one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means of a time-series analysis, in particular a nonlinear forecasting method which is based on concepts from chaos theory and appropriate statistical methods. We analyze two types of temporal signals, a local one and a global one, finding in both cases that the dynamical state of the gKS solution undergoes a transition from high-dimensional chaos to periodic pulsed oscillations through low-dimensional deterministic chaos with increasing the control parameter of the system. Our results demonstrate that the proposed nonlinear forecasting methodology allows to elucidate the dynamics of the system in terms of its predictability properties.
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