Frequency locking of periodic solutions to differential equations with impulsive perturbations

• Datum: 2022
• Hauptverfasser: Dvornyk, A. V., Tkachenko, V. I., Дворник, А. В., Ткаченко, В. I., Tkachenko, Viktor
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2022
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/7138
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.