Siberian Mathematical Journal

, Volume 30, Issue 4, pp 641–653 | Cite as

Conditions for auto-oscillations in nonlinear systems

  • É. A. Tomberg
  • V. A. Yakubovich


Nonlinear System 
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.

Literature Cited

  1. 1.
    V. A. Yakubovich, “Frequency conditions for oscillations in nonlinear systems with one stationary nonlinearity,” Sib. Mat. Zh.,14, No. 5, 1100–1129 (1973).Google Scholar
  2. 2.
    S. Smale, “A mathematical model of interaction of two cells utilizing the Turing equation,” in: Hopf Bifurcation and Its Applications [Russian translation], J. Marsden and M. McCracken (eds.), Mir, Moscow (1980), pp. 274–283.Google Scholar
  3. 3.
    A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, Stability of Nonlinear Systems with Nonunique Equilibria [in Russian], Nauka, Moscow (1978).Google Scholar
  4. 4.
    V. A. Yakubovich, “The method of matrix inequalities in the theory of stability of nonlinear control systems. I. Absolute stability of forced oscillations,” Avtomat. Telemekh.,25, No. 7, 1017–1029 (1964).Google Scholar
  5. 5.
    A. A. Voronov, Stability, Controllability, Observability [in Russian], Nauka, Moscow (1979).Google Scholar
  6. 6.
    A. V. Zharkov and V. A. Yakubovich, “A quadratic conditional absolute stability criterion and its application,” in: System Dynamics. Mathematical Methods of Theory of Oscillations [in Russian], Issue 12, Izd. Gor'k. Univ., Gor'kii (1977), pp. 54–66.Google Scholar
  7. 7.
    V. A. Yakubovich, “Methods of absolute stability theory,” in: Mathods of Study of Nonlinear Automatic Control Systems [in Russian], Nauka, Moscow (1975), pp. 74–180.Google Scholar
  8. 8.
    R. Field and M. Burger (eds.), Oscillations and Traveling Waves in Chemical Systems [Russian translation], Mir, Moscow (1988).Google Scholar
  9. 9.
    V. A. Yakubovich, “Absolute instability of nonlinear control systems. I. General frequency criteria,” Avtomat. Telemekh.,29, No. 12, 5–14 (1970).Google Scholar
  10. 10.
    V. M. Popov, Hyperstability of Automatic Systems [in Russian], Nauka, Moscow (1970).Google Scholar
  11. 11.
    P. Hartman, Ordinary Differential Equations, S. M. Hartman, MD (1973).Google Scholar
  12. 12.
    F. R. Gantmacher, Theory of Matrices, 2 vols., Chelsea Publ. Co., New York.Google Scholar
  13. 13.
    É. A. Tomberg, “A frequency dissipativity criterion in degenerate case for systems with several nonlinearities,” Vestn. Leningrad. Gos. Univ., Ser. Mat., Mekh., Astron., No. 3 (1989).Google Scholar
  14. 14.
    A. V. Nechitailo, “A frequency dissipativity criterion for systems with one nonlinearity,” Vestn. Leningrad. Gos. Univ., Dep. VINITI, No. 2423-76 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • É. A. Tomberg
  • V. A. Yakubovich

There are no affiliations available

Personalised recommendations