title: Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: reconstruction meeting with adaptation.
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.
authors.affiliation: School of Mathematical Sciences, Soochow University, Suzhou 215006, China.
authors.forename: Huanfei
authors.initials: H
authors.lastname: Ma
authors.forename: Wei
authors.initials: W
authors.lastname: Lin
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology; D000465:Algorithms; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009473:Neuronal Plasticity / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*