Phase Description Method to Time Averages in the Lorenz System
- 1 August 1986
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 76 (2) , 335-355
- https://doi.org/10.1143/ptp.76.335
Abstract
On the basis of the transformation to the rotating coordinates associated with the imbedded unstable limit cycles in the Lorenz system, we present a new representation for the long time averages, which may be applicable to any three-dimensional dissipative dynamical systems producing chaos. By employing the dynamics of the phases of the imbeddid limit cycles, we show that the time average is expressible in terms of two types of the weight factors; the residence time probability density and the factor inbersely proportional to the speed of the phase.Keywords
This publication has 5 references indexed in Scilit:
- Metastable chaos: The transition to sustained chaotic behavior in the Lorenz modelJournal of Statistical Physics, 1979
- On the statistical dynamics of the Lorenz modelJournal of Statistical Physics, 1979
- Statistical dynamics of the Lorenz modelJournal of Statistical Physics, 1976
- Deterministic Nonperiodic FlowJournal of the Atmospheric Sciences, 1963
- Finite Amplitude Free Convection as an Initial Value Problem—IJournal of the Atmospheric Sciences, 1962