Collective dynamical response of coupled oscillators with any network structure

Abstract

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.

4 pages, 2 figures

References in corpus (8)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Synchronization of two interacting populations of oscillators
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Collective Phase Sensitivity
• Neuronal synchrony during anaesthesia - A thalamocortical model
• Phase Response Curves of Coupled Oscillators
• Synchronization Engineering: Theoretical Framework and Application to Dynamical Clustering
• Perturbation Analysis of Complete Synchronization in Networks of Phase Oscillators

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