Static parametric fluctuations give nonstatistical behavior in uncoupled chaotic systems
- 1 January 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 49 (1) , R15-R18
- https://doi.org/10.1103/physreve.49.r15
Abstract
We show that an ensemble of logistic maps, with parameters distributed in some range inside a chaotic region, cannot be statistical. This is so because any parameter range for this map includes periodic windows. The effects of this periodicity in the averages of the system can be estimated, and are also apparent in the power spectra of average values. As a counterexample, we show that the behavior for tent maps, where chaotic regions do not include periodic windows, is statistical.Keywords
This publication has 13 references indexed in Scilit:
- Order in the turbulent phase of globally coupled mapsPhysica D: Nonlinear Phenomena, 1993
- Noisy uncoupled chaotic map ensembles violate the law of large numbersPhysical Review Letters, 1992
- Nonstatistical behavior of higher-dimensional coupled systemsPhysical Review A, 1992
- Nonstatistical behavior of coupled optical systemsPhysical Review A, 1992
- Mean field fluctuation of a network of chaotic elementsPhysica D: Nonlinear Phenomena, 1992
- Emergence of Effective Low-Dimensional Dynamics in the Macroscopic Behaviour of Coupled Map LatticesEurophysics Letters, 1992
- Noisy collective behaviour in deterministic cellular automataPhysica A: Statistical Mechanics and its Applications, 1992
- Evidence of Collective Behaviour in Cellular AutomataEurophysics Letters, 1991
- Globally coupled chaos violates the law of large numbers but not the central-limit theoremPhysical Review Letters, 1990
- Correlations and spectra of periodic chaos generated by the logistic parabolaJournal of Statistical Physics, 1981