Skip to main content
Log in

On the Theory of Synchronization of Dynamical Systems

  • Short Communications
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We prove theorems on the synchronization of dynamical systems with respect to all and part of the state variables in both the sense of the classical definition of synchronization (Blekhman) and the sense of Zubov; some illustrative examples are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Blekhman, I.I., Sinkhronizatsiya dinamicheskikh sistem (Synchronization of Dynamical Systems), Moscow: Nauka, 1971.

    MATH  Google Scholar 

  2. Buzlukova, O.A., Synchronous motions. Synchronism in small and in the whole, in Metody vozmushchenii v gomologicheskoi algebre i dinamika sistem (Perturbation Methods in Homological Algebra and Dynamics of Systems), Collection of Scientific Papers, Saransk: Mordovian Univ., 2004, pp. 41–45.

    Google Scholar 

  3. Vorotnikov, V.I. and Rumyantsev, V.V., Ustoichivost’ i upravlenie po chasti koordinat fazovogo vektora dinamicheskikh sistem: teoriya, metody i prilozheniya (Stability and Control with Respect to Part of Coordinates of the State Vector of Dynamical Systems: Theory, Methods, and Applications), Moscow: Nauchnyi Mir, 2001.

    MATH  Google Scholar 

  4. Vorotnikov, V.I., Theory of stability with respect to a part of the variables and the problem of coordinate synchronization for dynamical systems, Dokl. Phys., 2000, vol.45, no 12, pp. 685–689.

    Article  MathSciNet  Google Scholar 

  5. Zubov, V.I., Dinamika upravlyaemykh sistem (Dynamics of Controlled Systems), St. Petersburg: S.-Peterb. Gos. Univ., 2004.

    Google Scholar 

  6. Rumyantsev, V.V. and Oziraner, A.S., Ustoichivost’ i stabilizatsiya dvizheniya po otnosheniyu k chasti peremennykh (Stability and Stabilization of Motion with Respect to Part of the Variables), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  7. Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost’ nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with a Nonunique Equilibrium), Moscow: Nauka, 1978.

    MATH  Google Scholar 

  8. Leonov, G.A., Second Lyapunov method in the theory of state synchronization, Prikl. Mat. Mekh., 1976, vol.40, no. 2, pp. 238–244.

    Google Scholar 

  9. Malkin, I.G., Metody Lyapunova i Puankare v teorii nelineinykh kolebanii (Lyapunov and Poincare Methods in the Theory of Nonlinear Oscillations), Moscow: Gos. Izd. Tekh. Teor. Lit., 1949.

    MATH  Google Scholar 

  10. Malkin, I.G., Nekotorye zadachi teorii nelineinykh kolebanii (Several Problems of Theory of Nonlinear Oscillations), Moscow: Gos. Izd. Tekh. Teor. Lit., 1956.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Shchennikov.

Additional information

Original Russian Text © A.V. Shchennikov, V.N. Shchennikov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 12, pp. 1714–1718.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shchennikov, A.V., Shchennikov, V.N. On the Theory of Synchronization of Dynamical Systems. Diff Equat 54, 1674–1678 (2018). https://doi.org/10.1134/S0012266118120133

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266118120133

Navigation