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Stability of periodic clusters in globally coupled maps

Stability of periodic clusters in globally coupled maps

The phenomenon of partial synchronization, — or clustering, — in a system of globally coupled C 1 - smooth maps is analyzed. We prove stability of equally populated K-clustered states with period-n temporal dynamics, referred to as PnCK-states. For this, we first obtain formulas giving relation b...

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Bibliographic Details
Main Authors: Panchuk, A.A., Maistrenko, Y.L.
Format: Article
Language:English
Published: Інститут математики НАН України 2002
Series:Нелінійні коливання
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/175837
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Summary:The phenomenon of partial synchronization, — or clustering, — in a system of globally coupled C 1 - smooth maps is analyzed. We prove stability of equally populated K-clustered states with period-n temporal dynamics, referred to as PnCK-states. For this, we first obtain formulas giving relation between longitudinal and transverse nultipliers of the in-cluster periodic orbits and then, using these formulas, find exact parameter intervals for the transverse stability. We conclude that typically, for the symmetric PnCK-states, in-cluster stability implies transverse stability. Moreover, transverse stability can take place even if the incluster dynamics is unstable.

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