High-dimensional chaos in delayed dynamical systems

S  Lepri; G  Giacomelli; A  Politi; F T  Arecchi

doi:10.1016/0167-2789(94)90016-7

High-dimensional chaos in delayed dynamical systems

S Lepri, G Giacomelli, A Politi, F T Arecchi

Physics

Research output: Contribution to journal › Article › peer-review

87 Citations (Scopus)

Abstract

We introduce a general class of iterative delay maps to model high-dimensional chaos in dynamical systems with delayed feedback. The class includes as particular cases systems with a linear local dynamics. We report analytic and numerical results on the scaling laws of Lyapunov spectra with a number of degrees of freedom. Invariant measure is computed through a self-consistent Frobenius-Perron formalism, which allows also a recalculation of the maximum Lyapunov exponent in good agreement with the one measured directly.

Original language	English
Pages (from-to)	235-249
Number of pages	15
Journal	Physica. D, Nonlinear Phenomena
Volume	70
Issue number	3
DOIs	https://doi.org/10.1016/0167-2789(94)90016-7
Publication status	Published - 15 Jan 1994

Keywords

feedback
attractors

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10.1016/0167-2789(94)90016-7

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title = "High-dimensional chaos in delayed dynamical systems",

abstract = "We introduce a general class of iterative delay maps to model high-dimensional chaos in dynamical systems with delayed feedback. The class includes as particular cases systems with a linear local dynamics. We report analytic and numerical results on the scaling laws of Lyapunov spectra with a number of degrees of freedom. Invariant measure is computed through a self-consistent Frobenius-Perron formalism, which allows also a recalculation of the maximum Lyapunov exponent in good agreement with the one measured directly.",

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AU - Giacomelli, G

AU - Politi, A

AU - Arecchi, F T

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Y1 - 1994/1/15

N2 - We introduce a general class of iterative delay maps to model high-dimensional chaos in dynamical systems with delayed feedback. The class includes as particular cases systems with a linear local dynamics. We report analytic and numerical results on the scaling laws of Lyapunov spectra with a number of degrees of freedom. Invariant measure is computed through a self-consistent Frobenius-Perron formalism, which allows also a recalculation of the maximum Lyapunov exponent in good agreement with the one measured directly.

AB - We introduce a general class of iterative delay maps to model high-dimensional chaos in dynamical systems with delayed feedback. The class includes as particular cases systems with a linear local dynamics. We report analytic and numerical results on the scaling laws of Lyapunov spectra with a number of degrees of freedom. Invariant measure is computed through a self-consistent Frobenius-Perron formalism, which allows also a recalculation of the maximum Lyapunov exponent in good agreement with the one measured directly.

KW - feedback

KW - attractors

U2 - 10.1016/0167-2789(94)90016-7

DO - 10.1016/0167-2789(94)90016-7

M3 - Article

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VL - 70

SP - 235

EP - 249

JO - Physica. D, Nonlinear Phenomena

JF - Physica. D, Nonlinear Phenomena

IS - 3

ER -

High-dimensional chaos in delayed dynamical systems

Abstract

Keywords

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