Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory

Abstract

Optimal entrainment of limit-cycle oscillators by strong periodic inputs is studied on the basis of the phase-amplitude reduction and Floquet theory. Two methods for deriving the input waveforms that keep the system state close to the original limit cycle are proposed, which enable the use of strong inputs for entrainment. The first amplitude-feedback method uses feedback control to suppress deviations of the system state from the limit cycle, while the second amplitude-penalty method seeks an input waveform that does not excite large deviations from the limit cycle in the feedforward framework. Optimal entrainment of the van der Pol and Willamowski-Rössler oscillators with real or complex Floquet exponents are analyzed as examples. It is demonstrated that the proposed methods can achieve considerably faster entrainment and provide wider entrainment ranges than the conventional method that relies only on phase reduction.

arXiv comment37pages, 8 figures

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• Phase-based control of periodic fluid flows
• Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
• Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data
• Designing two-dimensional limit-cycle oscillators with prescribed trajectories and phase-response characteristics
• Sparse optimization of mutual synchronization in collectively oscillating networks