Abstract
A one-parameter periodic impulsive system of the second order is considered. The conditions for the appearance of the generic Andronov–Hopf bifurcation are discussed. It is shown that this bifurcation leads to the appearance of an almost periodic solution, the trajectory of which completely fills a certain annular region surrounding the rest point. Explicit formulas are also obtained that make it possible to calculate the numerical characteristic of the stability of an impulsive system in the critical case of a pair of complex conjugate multipliers of the monodromy matrix of the linear approximation in the vicinity of the rest point.
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Anashkin, O.V., Yusupova, O.V. Stability in the Critical Case and Bifurcations in Impulsive Systems. Lobachevskii J Math 42, 3574–3583 (2021). https://doi.org/10.1134/S1995080222030039
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DOI: https://doi.org/10.1134/S1995080222030039