Frequency locking of periodic solutions to differential equations with impulsive perturbations

  • A. V. Dvornyk Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev
  • V. I. Tkachenko Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev
Keywords: frequency locking, impulsive perturbation, periodic solution


UDC 517.9

We present sufficient conditions for the frequency locking of an orbitally asymptotically stable periodic solution of a system of autonomous differential equations with small impulsive perturbations. We introduce local coordinates in the neighborhood of stable invariant cycle and prove the existence of a piecewise smooth integral manifold of the perturbed impulsive system. The method of averaging for the impulsive system is applied to the investigation of the equation on the manifold and in order to deduce the conditions of frequency synchronisation.

Author Biography

A. V. Dvornyk, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev


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How to Cite
Dvornyk, A. V., and V. I. Tkachenko. “Frequency Locking of Periodic Solutions to Differential Equations With Impulsive Perturbations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 7, Aug. 2022, pp. 939 -60, doi:10.37863/umzh.v74i7.7138.
Research articles