Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the existence of piecewise-continuous separatrix curves for a certain class of pulse systems

  • 18 Accesses


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.


  1. 1.

    N. A. Perestyuk, “Invariant sets of a certain class of discontinuous dynamic systems,”Ukr. Mat. Zh.,36, No. 1, 63–68 (1984).

  2. 2.

    A. M. Samoilenko, “On the preservation of an invariant torus under perturbation,”Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 6, 1219–1240 (1970).

  3. 3.

    A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).

  4. 4.

    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).

  5. 5.

    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).

  6. 6.

    A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).

  7. 7.

    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).

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 580–585, May, 1994.

Rights and permissions

Reprints 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

Download citation


  • Differential Equation
  • Pulse System
  • Separatrix Curve
  • Pulse Influence