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Frequency Locking of Periodic Solutions to Differential Equations with Impulsive Perturbations

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Ukrainian Mathematical Journal Aims and scope

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

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. V. Dvornyk

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. I. Tkachenko

Authors
  1. A. V. Dvornyk
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  2. V. I. Tkachenko
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Correspondence to V. I. Tkachenko.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 7, pp. 939–960, July, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i7.7138.

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Dvornyk, A.V., Tkachenko, V.I. Frequency Locking of Periodic Solutions to Differential Equations with Impulsive Perturbations. Ukr Math J 74, 1073–1098 (2022). https://doi.org/10.1007/s11253-022-02121-2

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  • DOI: https://doi.org/10.1007/s11253-022-02121-2

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