The reservoir’s perspective on generalized synchronization

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Abstract

We employ reservoir computing for a reconstruction task in coupled chaotic systems, across a range of dynamical relationships including generalized synchronization. For a drive-response setup, a temporal representation of the synchronized state is discussed as an alternative to the known instantaneous form. The reservoir has access to both representations through its fading memory property, each with advantages in different dynamical regimes. We also extract signatures of the maximal conditional Lyapunov exponent in the performance of variations of the reservoir topology. Moreover, the reservoir model reproduces different levels of consistency where there is no synchronization. In a bidirectional coupling setup, high reconstruction accuracy is achieved despite poor observability and independent of generalized synchronization.
Original languageEnglish
Article number093133
JournalChaos: an interdisciplinary journal of nonlinear science
Volume29
Issue number9
DOIs
Publication statusPublished - 30 Sep 2019

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Generalized Synchronization
synchronism
Synchronization
Chaotic systems
Observability
Fading Memory
fading
Topology
Lyapunov Exponent
Chaotic System
Coupled System
Instantaneous
Data storage equipment
Signature
topology
signatures
exponents
Computing
Alternatives
Range of data

Cite this

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title = "The reservoir’s perspective on generalized synchronization",
abstract = "We employ reservoir computing for a reconstruction task in coupled chaotic systems, across a range of dynamical relationships including generalized synchronization. For a drive-response setup, a temporal representation of the synchronized state is discussed as an alternative to the known instantaneous form. The reservoir has access to both representations through its fading memory property, each with advantages in different dynamical regimes. We also extract signatures of the maximal conditional Lyapunov exponent in the performance of variations of the reservoir topology. Moreover, the reservoir model reproduces different levels of consistency where there is no synchronization. In a bidirectional coupling setup, high reconstruction accuracy is achieved despite poor observability and independent of generalized synchronization.",
author = "Thomas Lymburn and Walker, {David M.} and Michael Small and Thomas J{\"u}ngling",
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AB - We employ reservoir computing for a reconstruction task in coupled chaotic systems, across a range of dynamical relationships including generalized synchronization. For a drive-response setup, a temporal representation of the synchronized state is discussed as an alternative to the known instantaneous form. The reservoir has access to both representations through its fading memory property, each with advantages in different dynamical regimes. We also extract signatures of the maximal conditional Lyapunov exponent in the performance of variations of the reservoir topology. Moreover, the reservoir model reproduces different levels of consistency where there is no synchronization. In a bidirectional coupling setup, high reconstruction accuracy is achieved despite poor observability and independent of generalized synchronization.

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