Geodesic
Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium
Kybernetika, Tome 51 (2015) no. 2, pp. 347-373 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.14736/kyb-2015-2-0347
Classification : 34C15, 34D06, 34D35
Keywords: coupled oscillators; synchronization; invariant manifolds 
@article{10_14736_kyb_2015_2_0347,
     author = {Martins, Rog\'erio and Morais, Gon\c{c}alo},
     title = {Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium},
     journal = {Kybernetika},
     pages = {347--373},
     year = {2015},
     volume = {51},
     number = {2},
     doi = {10.14736/kyb-2015-2-0347},
     mrnumber = {3350567},
     zbl = {06487084},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-2-0347/}
}
TY  - JOUR
AU  - Martins, Rogério
AU  - Morais, Gonçalo
TI  - Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium
JO  - Kybernetika
PY  - 2015
SP  - 347
EP  - 373
VL  - 51
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-2-0347/
DO  - 10.14736/kyb-2015-2-0347
LA  - en
ID  - 10_14736_kyb_2015_2_0347
ER  - 
%0 Journal Article
%A Martins, Rogério
%A Morais, Gonçalo
%T Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium
%J Kybernetika
%D 2015
%P 347-373
%V 51
%N 2
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-2-0347/
%R 10.14736/kyb-2015-2-0347
%G en
%F 10_14736_kyb_2015_2_0347
Martins, Rogério; Morais, Gonçalo. Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium. Kybernetika, Tome 51 (2015) no. 2, pp. 347-373. doi: 10.14736/kyb-2015-2-0347

[1] Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics, Springer, 1977. | DOI | MR | Zbl

[2] Hatcher, A.: Algebraic Topology. Cambridge University Press, 2002. | DOI | MR | Zbl

[3] Horn, R., Johnson, C.: Topics in Matrix Analysis. Cambridge University Press, 1990. | DOI | MR | Zbl

[4] Katriel, G.: Synchronization of oscillators coupled through an environment. Physica D 237 (2008), 2933-2944. | DOI | MR | Zbl

[5] Margheri, A., Martins, R.: Generalized synchronization in linearly coupled time periodic systems. J. Differential Equations 249 (2010), 3215-3232. | DOI | MR

[6] Morais, G.: Dinâmica de Osciladores Acoplados. PhD Thesis, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2013.

[7] Pantaleone, J.: Synchronization of metronomes. Am. J. Phys. 70 (2002), 992-1000. | DOI

[8] Smith, R. A.: Poincaré index theorem concerning periodic orbits of differential equations. Proc. London Math. Soc. s3-48 (1984), 2, 341-362. | DOI | MR | Zbl

[9] Smith, R. A.: Massera's convergence theorem for periodic nonlinear differential equations. J. Math. Anal. Appl 120 (1986), 679-708. | DOI | MR | Zbl

[10] Wazewski, T.: Sur un principle topologique de l'examen de l'allure asymptotique des integrales des Equations differentielles ordinaires. Ann. Soc. Polon Math. 20 (1947), 279-313. | MR

Cité par Sources :