Multistability and the control of complexity

Ulrike Feudel, Celso Grebogi

Research output: Contribution to journalArticle

106 Citations (Scopus)

Abstract

We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (C) 1997 American Institute of Physics.

Original languageEnglish
Pages (from-to)597-604
Number of pages8
JournalChaos
Volume7
Issue number4
DOIs
Publication statusPublished - Dec 1997

Keywords

  • multiple steady-states
  • chaotic itinerancy
  • double crises
  • attractors
  • reactors
  • systems
  • array
  • map

Cite this

Multistability and the control of complexity. / Feudel, Ulrike; Grebogi, Celso.

In: Chaos, Vol. 7, No. 4, 12.1997, p. 597-604.

Research output: Contribution to journalArticle

Feudel, Ulrike ; Grebogi, Celso. / Multistability and the control of complexity. In: Chaos. 1997 ; Vol. 7, No. 4. pp. 597-604.
@article{7bb2710fa0c645fb9c9e918e45cf99e3,
title = "Multistability and the control of complexity",
abstract = "We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (C) 1997 American Institute of Physics.",
keywords = "multiple steady-states, chaotic itinerancy, double crises, attractors, reactors, systems, array, map",
author = "Ulrike Feudel and Celso Grebogi",
year = "1997",
month = "12",
doi = "10.1063/1.166259",
language = "English",
volume = "7",
pages = "597--604",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics",
number = "4",

}

TY - JOUR

T1 - Multistability and the control of complexity

AU - Feudel, Ulrike

AU - Grebogi, Celso

PY - 1997/12

Y1 - 1997/12

N2 - We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (C) 1997 American Institute of Physics.

AB - We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (C) 1997 American Institute of Physics.

KW - multiple steady-states

KW - chaotic itinerancy

KW - double crises

KW - attractors

KW - reactors

KW - systems

KW - array

KW - map

U2 - 10.1063/1.166259

DO - 10.1063/1.166259

M3 - Article

VL - 7

SP - 597

EP - 604

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 4

ER -