Abstract
Sufficient conditions for the existence of piecewise-continuous separatrix curves are obtained for a certain class of systems of differential equations with pulse influence for small ɛ ≥ 0.
Similar content being viewed by others
References
N. A. Perestyuk, “Invariant sets of a certain class of discontinuous dynamic systems,”Ukr. Mat. Zh.,36, No. 1, 63–68 (1984).
A. M. Samoilenko, “On the preservation of an invariant torus under perturbation,”Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 6, 1219–1240 (1970).
A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).
V. I. Tkachenko, “Green's function and the existence conditions for invariant sets of pulse systems,”Ukr. Mat. Zh.,41, No. 10, 1379–1383 (1989).
Yu. A. Mitropol'skii, A. M. Samoilenko, and V. L. Kulik,Study of Dichotomy of Linear Systems of Differential Equations by Using Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).
A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).
O. P. Svistun, “On the separatrix curves of a family of linear systems with pulse influence,”Ukr. Mat. Zh.,45, No. 12, 1682–1687 (1993).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 580–585, May, 1994.
Rights and permissions
About this article
Cite this article
Svistun, O.P. On the existence of piecewise-continuous separatrix curves for a certain class of pulse systems. Ukr Math J 46, 618–624 (1994). https://doi.org/10.1007/BF01058523
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058523