Super persistent chaotic transients in physical systems: Effect of noise on phase synchronization of coupled chaotic oscillators

Victor Andrade, Ying-Cheng Lai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2π's in parameter regimes where phase synchronization is expected in the absence of noise. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We provide heuristic arguments for the scaling law of the average transient lifetime and verify it using numerical examples from both the system of coupled Chua's circuits and that of coupled Rössler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizable systems.

Original languageEnglish (US)
Pages (from-to)2607-2619
Number of pages13
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume11
Issue number10
DOIs
StatePublished - Oct 2001

Fingerprint

Chaotic Oscillator
Phase Synchronization
Coupled Oscillators
Synchronization
Unstable
Coupled circuits
Chua's Circuit
Scaling laws
Time-average
Scaling Laws
White noise
Chaos theory
Slip
Periodic Orbits
Critical value
Continuous Time
Lifetime
Chaos
Dynamical systems
Discrete-time

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

@article{0721827a56bc425c87d13d6cb6244216,
title = "Super persistent chaotic transients in physical systems: Effect of noise on phase synchronization of coupled chaotic oscillators",
abstract = "A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2π's in parameter regimes where phase synchronization is expected in the absence of noise. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We provide heuristic arguments for the scaling law of the average transient lifetime and verify it using numerical examples from both the system of coupled Chua's circuits and that of coupled R{\"o}ssler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizable systems.",
author = "Victor Andrade and Ying-Cheng Lai",
year = "2001",
month = "10",
doi = "10.1142/S0218127401003723",
language = "English (US)",
volume = "11",
pages = "2607--2619",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "10",

}

TY - JOUR

T1 - Super persistent chaotic transients in physical systems

T2 - Effect of noise on phase synchronization of coupled chaotic oscillators

AU - Andrade, Victor

AU - Lai, Ying-Cheng

PY - 2001/10

Y1 - 2001/10

N2 - A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2π's in parameter regimes where phase synchronization is expected in the absence of noise. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We provide heuristic arguments for the scaling law of the average transient lifetime and verify it using numerical examples from both the system of coupled Chua's circuits and that of coupled Rössler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizable systems.

AB - A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2π's in parameter regimes where phase synchronization is expected in the absence of noise. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We provide heuristic arguments for the scaling law of the average transient lifetime and verify it using numerical examples from both the system of coupled Chua's circuits and that of coupled Rössler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizable systems.

UR - http://www.scopus.com/inward/record.url?scp=0035488686&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035488686&partnerID=8YFLogxK

U2 - 10.1142/S0218127401003723

DO - 10.1142/S0218127401003723

M3 - Article

AN - SCOPUS:0035488686

VL - 11

SP - 2607

EP - 2619

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 10

ER -