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Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators

Author

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  • Namura, Norihisa
  • Nakao, Hiroya

Abstract

We present a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit-cycle oscillators. Our method is based on phase reduction that provides a concise low-dimensional representation of the synchronization dynamics of mutually coupled oscillators, including the case where the coupling depends on past time series of the oscillators. We first describe a method for a pair of identical oscillators and then generalize it to the case of slightly nonidentical oscillators. The coupling function is designed in two optimization steps for the functional form and amplitude, where the amplitude is numerically optimized to minimize the average convergence time under a constraint on the total power. We perform numerical simulations of the synchronization dynamics with the optimized coupling functions using the FitzHugh–Nagumo and Rössler oscillators as examples. We show that the coupling function optimized by the present method can achieve global synchronization more efficiently than those obtained by the previous methods.

Suggested Citation

  • Namura, Norihisa & Nakao, Hiroya, 2024. "Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006325
    DOI: 10.1016/j.chaos.2024.115080
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