Stability of synchronized and clustered states in coupled piecewise linear maps
Parameter regions for different types of stability of synchronized and clustered states are obtained for two interacting ensembles of globally coupled one-dimensional piecewise linear maps. We analyze strong (asymptotic) and weak (Milnor) stability of the synchronized state, as well as its instabi...
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| Date: | 2004 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2004
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/177006 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Stability of synchronized and clustered states in coupled piecewise linear maps / I.V. Matskiv // Нелінійні коливання. — 2004. — Т. 7, № 2. — С. 217-228. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Parameter regions for different types of stability of synchronized and clustered states are obtained for
two interacting ensembles of globally coupled one-dimensional piecewise linear maps. We analyze strong
(asymptotic) and weak (Milnor) stability of the synchronized state, as well as its instability. We found that
the stability and instability regionsin the phase space depend only on parameters of the individualskew tent
map, and do not depend on the ensembles size. In the simplest nontrivial case of four coupled chaotic maps
we obtain stability regions for coherent and two-cluster states. The regions appear to be large enough to
provide an effective control of coherent and clustered chaotic regimes. Transition from desynchronization
to synchronization is identified to be qualitatively different in smooth and piecewise linear models. |
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