| Title:
|
Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium (English) |
| Author:
|
Martins, Rogério |
| Author:
|
Morais, Gonçalo |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
347-373 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented with a numerical study. (English) |
| Keyword:
|
coupled oscillators |
| Keyword:
|
synchronization |
| Keyword:
|
invariant manifolds |
| MSC:
|
34C15 |
| MSC:
|
34D06 |
| MSC:
|
34D35 |
| idZBL:
|
Zbl 06487084 |
| idMR:
|
MR3350567 |
| DOI:
|
10.14736/kyb-2015-2-0347 |
| . |
| Date available:
|
2015-06-19T15:27:40Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144303 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Morais, G.: Dinâmica de Osciladores Acoplados..PhD Thesis, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2013. |
| Reference:
|
[7] Pantaleone, J.: Synchronization of metronomes..Am. J. Phys. 70 (2002), 992-1000. 10.1119/1.1501118 |
| Reference:
|
[8] Smith, R. A.: Poincaré index theorem concerning periodic orbits of differential equations..Proc. London Math. Soc. s3-48 (1984), 2, 341-362. Zbl 0509.34046, MR 0729074, 10.1112/plms/s3-48.2.341 |
| Reference:
|
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| Reference:
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| . |
