Extracting unstable periodic orbits from chaotic time series data
نویسندگان
چکیده
Paul So, 1,2 Edward Ott, 2,* Tim Sauer, 3 Bruce J. Gluckman, 4,1 Celso Grebogi, 2,† and Steven J. Schiff 1 Center for Neuroscience, Children’s Research Institute, Children’s National Medical Center and the George Washington University, NW, Washington, D.C. 20010 Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 Department of Mathematics, The George Mason University, Fairfax, Virginia 22030 Naval Surface Warfare Center, Carderock Division, Bethesda, Maryland 20054-5000 ~Received 27 January 1997!
منابع مشابه
Detecting unstable periodic orbits from transient chaotic time series
We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of f...
متن کاملAnalyses of transient chaotic time series.
We address the calculation of correlation dimension, the estimation of Lyapunov exponents, and the detection of unstable periodic orbits, from transient chaotic time series. Theoretical arguments and numerical experiments show that the Grassberger-Procaccia algorithm can be used to estimate the dimension of an underlying chaotic saddle from an ensemble of chaotic transients. We also demonstrate...
متن کاملDetecting unstable periodic orbits in high-dimensional chaotic systems from time series: reconstruction meeting with adaptation.
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 ...
متن کاملRecent Developments in Chaotic Time Series Analysis
In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing. A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical in...
متن کاملRecurrence plots and unstable periodic orbits.
A recurrence plot is a two-dimensional visualization technique for sequential data. These plots are useful in that they bring out correlations at all scales in a manner that is obvious to the human eye, but their rich geometric structure can make them hard to interpret. In this paper, we suggest that the unstable periodic orbits embedded in a chaotic attractor are a useful basis set for the geo...
متن کاملUnstable Periodic Orbit Analysis of Histograms of Chaotic Time Series
Using the Lorenz equations, we have investigated whether unstable periodic orbits (UPOs) associated with a strange attractor may predict the occurrence of the robust sharp peaks in histograms of some experimental chaotic time series. Histograms with sharp peaks occur for the Lorenz parameter value r = 60.0 but not for r = 28.0, and the sharp peaks for r = 60.0 do not correspond to any single hi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997