مرکز منطقه ای اطلاع رساني علوم و فناوري - Necessary and sufficient conditions for synchronization of nonlinear oscillators with a given class of coupling

DocumentCode :

1178762

Title :

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.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=1178762