2015/03/13 by Kestutis Pyragas, Pyragas, Kestutis, Viktor Novičenko +1
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD
paper · pdf · doi:10.48550/arxiv.1503.04041
arxiv created 2015/06/05 · arxiv updated 2015/06/08
The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible only when this frequency is higher (lower) than the natural frequency of the oscillator. Also, by using the Pontryagin maximum principle, we have derived an optimal waveform of the perturbation that ensures an entrainment of the oscillator with minimal power. The theoretical results are demonstrated with the Stuart-Landau oscillator and model neurons.