Hierarchical Abstraction of Phase Response Curves of Synchronized Systems of Coupled Oscillators

2011/06/16 by Jaijeet Roychowdhury, Roychowdhury, Jaijeet
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Quantitative Methods (q-bio.QM) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1106.3247

openalex publication_date 2011/06/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that a group of injection-locked oscillators, each modelled using a nonlinear phase macromodel, responds as a single oscillator to small external perturbations. More precisely, we show that any group of injection-locked oscillators has a single effective PRC [1] or PPV [2], [3] that characterises its phase/timing response to small external perturbations. This result constitutes a foundation for understanding and predicting synchronization/timing hierarchically in large, complex systems that arise in nature and engineering.

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