Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators

Abstract

Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of cross-diffusion coupling matrices between the oscillators, we consider optimization of mutual coupling signals to maximize the linear stability of the synchronized state, which are functionals of the past time sequences of the oscillator states. For the case of linear coupling, optimization of the delay time and linear filitering of coupling signals are considered. For the case of nonlinear coupling, general drive-response coupling is considered, and the optimal response and driving functions are derived. The theoretical results are exemplified by numerical simulations.

arXiv comment13pages,9 figures

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Cited by in corpus (9)

• Semiclassical Phase Reduction Theory for Quantum Synchronization
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• Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
• Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators
• A Central Pattern Generator Network for Simple Control of Gait Transitions in Hexapod Robots based on Phase Reduction
• Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators
• Phase-Amplitude Reduction and Optimal Phase Locking of Collectively Oscillating Networks
• Sparse optimization of mutual synchronization in collectively oscillating networks
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators