#### For citation:

Mishchenko M. A., Zhukova N. S., Polovinkin A. V., Matrosov V. V. Excitation of phase-controlled oscillator by pulse sequence. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2021, vol. 29, iss. 2, pp. 240-253. DOI: 10.18500/0869-6632-2021-29-2-240-253

# Excitation of phase-controlled oscillator by pulse sequence

The purpose of this work is to study the dynamics of phase-controlled oscillator in excitable mode under rectangular pulse train forcing. The excitable system is a system having a stable equilibrium and a large amplitude periodic pseudo-orbit passing near the equilibrium. Methods. In this paper, the dynamics of the generator under periodic or Poisson rectangular pulse train stimulation is studied by numerical simulation. Different values are proposed to characterize statistics of the oscillator’s responses on different number of stimulating pulses. Results. The role of amplitude and period of external forcing on generator excitation is studied. Relative frequency of the oscillator responses depends on the amplitude of stimulating pulses. Phase-controlled oscillator’s responses are synchronized with different rational relations to number of stimulating pulses depending on the amplitude of the pulses. The inter-pulse intervals of the oscillator are not completely rational to inter-pulse intervals of stimulating train in contrast to relative frequency of the oscillator responses. The Poisson pulse train stimulation gives nearly the same statistics of the oscillator’s responses as periodic forcing. Conclusion. Detailed study of the dynamics of phase-controlled oscillator in excitable mode under rectangular pulse train forcing is conducted. Different ways of the oscillator’s responses characterization shows the strong dependence on the amplitude of stimulating pulses but much weaker dependence on inter-pulse intervals of stimulating train. The most informative characteristics is a ratio between inter-pulse intervals of oscillator responses and stimulating train.

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