One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures

Vladimir N. Belykh; Erik Mosekilde

doi:10.1103/PhysRevE.54.3196

One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures

Vladimir N. Belykh, Erik Mosekilde

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Abstract

The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed.

Original language	English
Journal	Physical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume	54
Issue number	4
Pages (from-to)	3196-3203
ISSN	1063-651X
DOIs	https://doi.org/10.1103/PhysRevE.54.3196
Publication status	Published - 1996

Bibliographical note

Copyright (1996) American Physical Society.

Keywords

SYSTEMS
NETWORK
TRAVELING WAVES
PATTERNS
ELEMENTS
STABILITY
SPATIOTEMPORAL INTERMITTENCY
PERIODIC-ORBITS

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Cite this

Belykh, V. N., & Mosekilde, E. (1996). One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 54(4), 3196-3203. https://doi.org/10.1103/PhysRevE.54.3196

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T1 - One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures

AU - Belykh, Vladimir N.

AU - Mosekilde, Erik

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Y1 - 1996

N2 - The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed.

AB - The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed.

KW - SYSTEMS

KW - NETWORK

KW - TRAVELING WAVES

KW - PATTERNS

KW - ELEMENTS

KW - STABILITY

KW - SPATIOTEMPORAL INTERMITTENCY

KW - PERIODIC-ORBITS

U2 - 10.1103/PhysRevE.54.3196

DO - 10.1103/PhysRevE.54.3196

M3 - Journal article

VL - 54

SP - 3196

EP - 3203

JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

SN - 2470-0045

IS - 4

ER -