ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Ryskin N. M., Khavroshin O. S. Controlling chaos in Ikeda system. Spatio–temporal model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 2, pp. 87-98. DOI: 10.18500/0869-6632-2009-17-2-87-98

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Russian
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Article
UDC: 
537.86:87/530.182

Controlling chaos in Ikeda system. Spatio–temporal model

Autors: 
Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Khavroshin Oleg Sergeevich, Saratov State University
Abstract: 

The method for controlling chaos in a ring resonator filled with a medium with cubic phase nonlinearity (Ikeda system), suggested in [1], is investigated within the framework of a distributed spatio-temporal model described by a Nonlinear Schrodinger Equation with time-delayed boundary condition. Numerical results are presented which confirm the capability of the suggested method. For the case of weakly dispersive nonlinear medium, the results are in good agreement with the approximate theory based on the return map [1]. In the case of strong dispersion, when the non-stationary behavior is determined mainly by the modulation instability, the dynamics is more complicated due to competition of different resonator eigenmodes. It is demonstrated, that proper adjustment of the control feedback parameters allows suppressing self-modulation oscillations and provides stable single-frequency operation in a broad range of parameters.

Reference: 
  1. Ryskin NM, Havroshin OS. Controlling chaos in Ikeda system. Symplified discrete map model. Izvestiya VUZ. Applied Nonlinear Dynamics. 2009;17(2):66–86. DOI: 10.18500/0869-6632-2009-17-2-66-86.
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Received: 
04.09.2008
Accepted: 
04.09.2008
Published: 
30.06.2009
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