TY - JOUR
AU - A. V. Dvornyk
AU - V. I. Tkachenko
PY - 2022/08/09
Y2 - 2023/03/27
TI - Frequency locking of periodic solutions to differential equations with impulsive perturbations
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 74
IS - 7
SE - Research articles
DO - 10.37863/umzh.v74i7.7138
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7138
AB - UDC 517.9We 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.
ER -