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Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: reconstruction meeting with
Huanfei Ma1, Wei Lin, Ying-Cheng Lai
1School of Mathematical Sciences, Soochow University, Suzhou 215006, China.
Abstract:
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.
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