Open AccessA numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators
Author(s) -
Richard H. Rand,
Asok K. Sen
Publication year - 2003
Publication title -
communications on pure andamp applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2003.2.567
Subject(s) - phase (matter) , physics , coupling (piping) , instability , stability (learning theory) , group delay and phase delay , mode (computer interface) , van der pol oscillator , plane (geometry) , relaxation (psychology) , mechanics , quantum mechanics , mathematics , nonlinear system , computer science , geometry , materials science , telecommunications , psychology , social psychology , bandwidth (computing) , machine learning , metallurgy , operating system
In this paper we examine the dynamics of two time-delay coupled relaxation oscillators of the van der Pol type. By integrating the governing dieren tial-delay equations numerically, we nd the various phase-locked mo- tions including the in-phase and out-of-phase modes. Our computations reveal that depending on the strength of coupling ( ) and the amount of time-delay ( ), the in-phase (out-of-phase) mode may be stable or unstable. There are also values of and for which the in-phase and out-of-phase modes are both stable leading to birhythmicity. The results are illustrated in the - parameter plane. Near the boundaries between stability and instability of the in-phase (out-of-phase) mode, many other types of phase-locked motions can occur. Several examples of these phase-locked states are presented.
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