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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
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).
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 580–585, May, 1994.
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
- Differential Equation
- Pulse System
- Separatrix Curve
- Pulse Influence