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Center for Nonlinear Studies |
Networks of coupled dynamical elements exhibiting collective oscillations often play important functional roles in real-world systems. We propose a method of dimensionality reduction for such networks by extending the classical phase reduction method for nonlinear limit-cycle oscillators. By projecting the network state to a single phase variable, a simple one-dimensional phase equation describing the collective oscillation of the network is derived. The derived phase equation is general and can be used in analyzing and controlling collectively oscillating networks subjected to weak driving signals. As a simple example, synchronization between collectively oscillating random networks of heterogeneous neural oscillators is analyzed.
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