Collective dynamical response of coupled oscillators with any network structure

Details Collective dynamical response of coupled oscillators with any network structure Collective dynamical response of coupled oscillators with any network structure

2008-11-30

arxiv.org/abs/0812.0118v1

Physical Review E 80, 036207 (2009)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

4 pages, 2 figures

Scientific paper

10.1103/PhysRevE.80.036207

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is also developed. General formulae for the collective phase sensitivity and the effective phase coupling between the oscillator networks are found. Our theory is applicable to a wide variety of oscillator networks undergoing frequency synchronization. Any network structure can systematically be treated. A few examples are given to illustrate our theory.

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