Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series

Journal Article · Thu Oct 01 00:00:00 EDT 1998 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.81.3375· OSTI ID:663737

Zoldi, S M ^[1]

---

1. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

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 a histogram derived from any single UPO. However, we show that histograms derived from the time series of a non-Axiom-A chaotic system can be accurately predicted by an escape-time weighting of UPO histograms. {copyright} {ital 1998} {ital The American Physical Society}

• DOE Contract Number: FG05-94ER25214
• OSTI ID: 663737
• Journal Information: Physical Review Letters, Vol. 81, Issue 16; Other Information: PBD: Oct 1998
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DYNAMICS
TIME-SERIES ANALYSIS
PHASE SPACE
ATTRACTORS
BIFURCATION
LIMIT CYCLE