Necessary and sufficient conditions for synchronization of nonlinear oscillators with a given class of coupling

Author

Grattarola, M. ; Torre, V.

Volume

Issue

fYear

1977

fDate

4/1/1977 12:00:00 AM

Firstpage

209

Lastpage

215

Abstract

Necessary and sufficient conditions are provided for phase synchronization of systems of identical nonlinear oscillators. The oscillators considered are described by the set of equations $\\dot{f}_i=f_1(x_i,y_i,\\mu)$ $dot{y}_i= f_2(x_i,y_i,\\mu)i= 1,\\cdots ,n$ . The type of coupling considered is $\\dot{x}_i = f_1 (x_i,y_i,\\mu) + \\Sigma _{j=1}^{n} g_1(x_j- x_i)$ $\\dot{y}_i = f_2(x_i,y_i,\\mu) + \\Sigma _{j=1}^{n} g_2(y_j-y_i)$ where $g_1,g_2 \\in C^2(R)$ and $g_1(0)=g_2(0)=0$ . Our approach is not based on the asymptotic methods of Mitropolsky and Bogoliubov and the coupling can be arbitrarily large. The conditions can be used successfully in several cases and some of the results can be extended to systems of slightly different oscillators.

Keywords

Nonlinear oscillators; Nonlinear systems; Synchronization; Biology; Circuits and systems; Couplings; Helium; Hydrogen; Limit-cycles; Nonlinear equations; Oscillators; Sufficient conditions;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/TCS.1977.1084326

Filename

1084326

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1178762