Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: reconstruction meeting with adaptation.
Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: reconstruction meeting with adaptation.
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DOI：
10.1103/physreve.87.050901
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
Huanfei Ma;Wei Lin;Y. Lai
中科院分区：
文献类型：
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作者：
Huanfei Ma;Wei Lin;Y. Lai
仅基于时间序列的混沌系统的不稳定周期轨道检测是非线性动力学中一个基本但极具挑战性的问题。以前的方法是适用的，但主要适用于低维混沌系统。我们开发了一个框架，集成了神经网络近似理论和自适应同步，以解决高维混沌系统中基于时间序列的upo检测问题。给出了从经典的麦基-格拉斯方程求upo的一个例子。
Detecting unstable periodic orbits (UPOs) in chaotic systems based solely on time series is a fundamental but extremely challenging problem in nonlinear dynamics. Previous approaches were applicable but mostly for low-dimensional chaotic systems. We develop a framework, integrating approximation theory of neural networks and adaptive synchronization, to address the problem of time-series-based detection of UPOs in high-dimensional chaotic systems. An example of finding UPOs from the classic Mackey-Glass equation is presented.