Transverse instability and riddled basins in a system of two coupled logistic maps

Yu.L. Maistrenko; V.L. Maistrenko; A. Popovich; Erik Mosekilde

doi:10.1103/PhysRevE.57.2713

Transverse instability and riddled basins in a system of two coupled logistic maps

Yu.L. Maistrenko, V.L. Maistrenko, A. Popovich, Erik Mosekilde

National Academy of Sciences of Ukraine

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Abstract

The paper examines the conditions for the appearance of riddled basins of attraction for a system of two symmetrically coupled logistic maps. We determine the regions in parameter space where the transverse Lyapunov exponent is negative and obtain the bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the synchronized chaotic state. The changes in the attractor and its basin of attraction when scanning accross the riddling and blowout bifurcations are explained.

Original language	English
Journal	Physical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume	57
Issue number	3
Pages (from-to)	2713-2724
ISSN	1063-651X
DOIs	https://doi.org/10.1103/PhysRevE.57.2713
Publication status	Published - 1998

Bibliographical note

Copyright (1998) by the American Physical Society.

Keywords

SADDLE
STABILITY THEORY
CHAOTIC ATTRACTORS
INTERMITTENCY
DYNAMICAL-SYSTEMS
SYNCHRONIZED MOTION
BIFURCATION
PERIODIC-ORBITS
OSCILLATOR SYSTEMS

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title = "Transverse instability and riddled basins in a system of two coupled logistic maps",

abstract = "The paper examines the conditions for the appearance of riddled basins of attraction for a system of two symmetrically coupled logistic maps. We determine the regions in parameter space where the transverse Lyapunov exponent is negative and obtain the bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the synchronized chaotic state. The changes in the attractor and its basin of attraction when scanning accross the riddling and blowout bifurcations are explained.",

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author = "Yu.L. Maistrenko and V.L. Maistrenko and A. Popovich and Erik Mosekilde",

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journal = "Physical Review E",

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T1 - Transverse instability and riddled basins in a system of two coupled logistic maps

AU - Maistrenko, Yu.L.

AU - Maistrenko, V.L.

AU - Popovich, A.

AU - Mosekilde, Erik

N1 - Copyright (1998) by the American Physical Society.

PY - 1998

Y1 - 1998

N2 - The paper examines the conditions for the appearance of riddled basins of attraction for a system of two symmetrically coupled logistic maps. We determine the regions in parameter space where the transverse Lyapunov exponent is negative and obtain the bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the synchronized chaotic state. The changes in the attractor and its basin of attraction when scanning accross the riddling and blowout bifurcations are explained.

AB - The paper examines the conditions for the appearance of riddled basins of attraction for a system of two symmetrically coupled logistic maps. We determine the regions in parameter space where the transverse Lyapunov exponent is negative and obtain the bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the synchronized chaotic state. The changes in the attractor and its basin of attraction when scanning accross the riddling and blowout bifurcations are explained.

KW - SADDLE

KW - STABILITY THEORY

KW - CHAOTIC ATTRACTORS

KW - INTERMITTENCY

KW - DYNAMICAL-SYSTEMS

KW - SYNCHRONIZED MOTION

KW - BIFURCATION

KW - PERIODIC-ORBITS

KW - OSCILLATOR SYSTEMS

U2 - 10.1103/PhysRevE.57.2713

DO - 10.1103/PhysRevE.57.2713

M3 - Journal article

VL - 57

SP - 2713

EP - 2724

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 3

ER -

Transverse instability and riddled basins in a system of two coupled logistic maps

Abstract

Bibliographical note

Keywords

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