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We propose a general method for optimizing periodic input waveforms forglobal entrainment of weakly forced limit-cycle oscillators based on phasereduction and nonlinear programming. We derive averaged phase dynamics from themathematical model of a limit-cycle oscillator driven by a weak periodic inputand optimize the Fourier coefficients of the input waveform to maximizeprescribed objective functions. In contrast to the optimization methods thatrely on the calculus of variations, the proposed method can be applied to awider class of optimization problems including global entrainment objectives.As an illustration, we consider two optimization problems, one for achievingfast global convergence of the oscillator to the entrained state and the otherfor realizing prescribed global phase distributions in a population ofidentical uncoupled noisy oscillators. We show that the proposed method cansuccessfully yield optimal input waveforms to realize the desired states inboth cases.

Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators