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...
Збережено в:
| Видавець: | Інститут математики НАН України |
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| Дата: | 2002 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2002
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/175837 |
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| Цитувати: | Stability of periodic clusters in globally coupled maps / A.A. Panchuk, Y.L. Maistrenko // Нелінійні коливання. — 2002. — Т. 5, № 3. — С. 334-345. — Бібліогр.: 15 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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