Automation and Remote Control

, Volume 62, Issue 8, pp 1240–1258 | Cite as

Method of Radial Drift for Qualitative Study of the Properties of the Nonlinear Dynamic Systems. III. On Existence of Invariant Closed Contours

  • V. P. Zhukov


Consideration was given to existence of the invariant closed contours of the nonlinear autonomous dynamic systems, that is, the closed contours consisting wholly of the trajectories of dynamic systems obeying the ordinary nonlinear vector differential equations of an arbitrary order. The structure of these contours was studied, and their classification was elaborated. Efficient conditions for nonexistence and existence of the invariant contours were obtained. Studies were carried out using the method of radial drift.


Differential Equation Dynamic System Mechanical Engineer Nonlinear Dynamic System Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andronov, A.A., Vitt, A.A., and Khaikin, S.E., Teoriya kolebanii (Theory of Oscillations), Moscow: Fizmatgiz, 1959.Google Scholar
  2. 2.
    Matematicheskaya entsiklopediya (Mathematical Encyclopedia), Moscow: Sovetskaya Entsiklopediya, 1977, vol. 1.Google Scholar
  3. 3.
    Bautin, N.N. and Leontovich E.A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti (Methods and Techniques for Qualitative Study of the Dynamic Systems on Plane), Moscow: Nauka, 1976.Google Scholar
  4. 4.
    Zhukov, V.P., On Periodic Modes in Nonlinear Systems, Avtom. Telemekh., 1981, no. 7, pp. 45-50.Google Scholar
  5. 5.
    Zhukov, V.P., Method of Radial Drift for Qualitative Study of the Properties of the Nonlinear Dynamic Systems. I, Avtom. Telemekh., 2000, no. 11, pp. 69-83.Google Scholar
  6. 6.
    Korn, G.A. and Korn, T.M., Mathematical Handbook for Scientists and Engineers, New York: McGraw-Hill, 1968. Translated under the title Spravochnik po matematike, Moscow: Nauka, 1977.Google Scholar
  7. 7.
    Luzin, N.N., Teoriya funktsii deistvitel'nogo peremennogo (Theory of the Functions of Real Variable), Moscow: Uchpedgiz, 1948.Google Scholar
  8. 8.
    Shilov, G.E., Matematicheskii analiz (funktsii odnogo peremennogo) (Mathematical Analysis (Functions of One Variable), Moscow: Nauka, 1969.Google Scholar
  9. 9.
    Kuratowsky, K., Topology, New York: Academic, 1966, vol. 2. Translated under the title Topologiya, Moscow: Mir, 1969, vol. 2.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • V. P. Zhukov
    • 1
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

Personalised recommendations