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The European Physical Journal D

, Volume 62, Issue 1, pp 57–66 | Cite as

Dynamics of two coupled chaotic systems driven by external signals

  • H. ManciniEmail author
  • G. Vidal
Article

Abstract.

Setting-up a controlled or synchronized state in a space-time chaotic structure targeting an unstable periodic orbit is a key feature of many problems in high dimensional physical, electronics, biological and ecological systems (among others). Formerly, we have shown numerically and experimentally that phase synchronization [M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 4193 (1997)] can be achieved in time dependent hydrodynamic flows [D. Maza, A. Vallone, H.L. Mancini, S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2000)]. In that case the flow was generated in a small container with inhomogeneous heating in order to have a single roll structure produced by a Bénard-Marangoni instability [E.L. Koshmieder, Bénard Cells and Taylor Vortices (Cambridge University Press, 1993)]. Phase synchronization was achieved by a small amplitude signal injected at a subharmonic frequency obtained from the measured Fourier temperature spectrum. In this work, we analyze numerically the effects of driving two previously synchronized chaotic oscillators by an external signal. The numerical system represents a convective experiment in a small container with square symmetry, where boundary layer instabilities are coupled by a common flow. This work is an attempt to control this situation and overcome some difficulties to select useful frequency values for the driving force, analyzing the influence of different harmonic injection signals on the synchronization in a system composed by two identical chaotic Takens-Bogdanov equations (TBA and TBB) bidirectionally coupled.

Keywords

Chaotic System Fourier Spectrum Harmonic Signal Complete Synchronization Unstable Periodic Orbit 
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.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Instituto de Física, Universidad de NavarraPamplonaSpain

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