Dynamics of two coupled chaotic systems driven by external signals |
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Authors: | H Mancini G Vidal |
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Institution: | (1) Nonlinear and Statistical Physics Research Group, Department of Physics, Olabisi Onabanjo University, P.M.B. 2002, Ago-Iwoye, Nigeria;(2) Department of Physics, College of Natural Sciences, University of Agriculture, Abeokuta, Nigeria |
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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. |
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Keywords: | |
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