Noise-induced chaos

A consequence of long deterministic transients

Tamas Tel, Ying-Cheng Lai, Marton Gruiz

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We argue that transient chaos in deterministic dynamical systems is a major source of noise-induced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractality. The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.

Original languageEnglish
Pages (from-to)509-520
Number of pages12
JournalInternational Journal of Bifurcation and Chaos
Volume18
Issue number2
DOIs
Publication statusPublished - Feb 2008

Keywords

  • noise-induced chaos
  • population dynamics
  • transient chaos
  • nonattracting chaotic sets
  • fractal dimension
  • time-series analysis
  • population-dynamics
  • systems
  • unpredictability
  • attractors

Cite this

Noise-induced chaos : A consequence of long deterministic transients. / Tel, Tamas; Lai, Ying-Cheng; Gruiz, Marton.

In: International Journal of Bifurcation and Chaos, Vol. 18, No. 2, 02.2008, p. 509-520.

Research output: Contribution to journalArticle

Tel, Tamas ; Lai, Ying-Cheng ; Gruiz, Marton. / Noise-induced chaos : A consequence of long deterministic transients. In: International Journal of Bifurcation and Chaos. 2008 ; Vol. 18, No. 2. pp. 509-520.
@article{b0068548740e4e31980f4825e78d4dc6,
title = "Noise-induced chaos: A consequence of long deterministic transients",
abstract = "We argue that transient chaos in deterministic dynamical systems is a major source of noise-induced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractality. The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.",
keywords = "noise-induced chaos, population dynamics, transient chaos, nonattracting chaotic sets, fractal dimension, time-series analysis, population-dynamics, systems, unpredictability, attractors",
author = "Tamas Tel and Ying-Cheng Lai and Marton Gruiz",
year = "2008",
month = "2",
doi = "10.1142/S0218127408020422",
language = "English",
volume = "18",
pages = "509--520",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "2",

}

TY - JOUR

T1 - Noise-induced chaos

T2 - A consequence of long deterministic transients

AU - Tel, Tamas

AU - Lai, Ying-Cheng

AU - Gruiz, Marton

PY - 2008/2

Y1 - 2008/2

N2 - We argue that transient chaos in deterministic dynamical systems is a major source of noise-induced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractality. The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.

AB - We argue that transient chaos in deterministic dynamical systems is a major source of noise-induced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractality. The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.

KW - noise-induced chaos

KW - population dynamics

KW - transient chaos

KW - nonattracting chaotic sets

KW - fractal dimension

KW - time-series analysis

KW - population-dynamics

KW - systems

KW - unpredictability

KW - attractors

U2 - 10.1142/S0218127408020422

DO - 10.1142/S0218127408020422

M3 - Article

VL - 18

SP - 509

EP - 520

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 2

ER -