Coupling-induced periodic windows in networked discrete-time systems

Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit oscillates chaotically if in isolation. Surprisingly, the mechanism...

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Bibliographic Details
Published in:arXiv.org 2021-12
Main Authors: Hallier, Leonard, Medeiros, Everton S, Mihara, Antonio, Medrano-T, Rene O, Zakharova, Anna
Format: Article
Language:English
Subjects:
Discrete time systems
Nonlinear systems
Parameters
Stability
Windows (intervals)
Online Access:Get full text
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Summary:Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit oscillates chaotically if in isolation. Surprisingly, the mechanism in which the network interaction replaces chaos by periodicity is still poorly understood. Here, we show that such an onset of regularity can occur via replication of periodic windows. This phenomenon multiplies the stability domains in the system parameter space, not only suppressing chaos but also making the network less vulnerable to external disturbances such as shocks and noise. Moreover, we observe that the network cluster synchronizes for the parameters corresponding to the replica periodic windows. To confirm these observations, we employ the formalism of the master stability function demonstrating that the complete synchronized state is indeed transversally unstable in the replica windows.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.07672