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Existence and stability of periodic solutions for chains of connected oscillators

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Abstract

We consider a nonlinear system of difference equations. This system corresponds to chains of N symmetrically connected oscillators with sufficiently general type of connection, which includes, among others, local and global connection. We prove a theorem on the existence and stability of space-time periodic solutions of such systems for sufficiently small values of the parameter of connection ɛ.

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References

  1. K. Koneko, Collapse of Tori and Genesis of Chaos in Disspative Systems, World Scientific, Singapore (1986).

    Google Scholar 

  2. L. A. Bunimovich, R. Livi, G. Martinez-Mekler, and S. Ruffo, “Coupled trivial maps,” Chaos, 2, No. 3, 283–291 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  3. V. S. Afraimovich and L. A. Bunimovich, “Simplest structures in coupled map lattices and their stability,” Rand. Comput. Dynamics, 1, 423–444 (1993).

    MATH  MathSciNet  Google Scholar 

  4. G. Giberty and C. Vernia, “On the presence of normally attracting manifolds containing periodic or quasiperiodic orbits in coupled map lattices,” Int. J. Bifurcation Chaos, 3, No. 6, 1503–1514 (1993).

    Article  Google Scholar 

  5. A. S. Pikovsky and J. Kurth, “Do globally coupled maps really violate the law of large numbers?” Phys. Rev. Lett., 72, No. 11, 1644–1646 (1994).

    Article  Google Scholar 

  6. G. Perez, S. Sinha, and H. A. Gerdeira, “Non-statistical behavior of coupled optical systems,” Phys. Rev. A., 45, No. 15, 5469–5477 (1992).

    Article  Google Scholar 

  7. A. N. Sharkovsky, Yu. L. Maistrenko, and E. Yu. Romanenko, Difference Equations and Their Applications, Kluwer, Dordrecht (1993).

    Google Scholar 

  8. Yu. L. Maistrenko, E. Yu. Romanenko, and A. N. Sharkovsky, “Integro-difference equations and dynamics of the size of populations,” Differents. Uravn. Primen., 29, 69–77 (1981).

    MATH  Google Scholar 

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Authors
  1. Yu. L. Maistrenko
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  2. A. V. Popovich
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7. pp. 943–950, July, 1997.

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Maistrenko, Y.L., Popovich, A.V. Existence and stability of periodic solutions for chains of connected oscillators. Ukr Math J 49, 1058–1066 (1997). https://doi.org/10.1007/BF02528751

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  • DOI: https://doi.org/10.1007/BF02528751

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