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

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Ryskin N. M., Khavroshin O. S. Controlling chaos in Ikeda system. Symplified discrete map model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 2, pp. 66-86. DOI: 10.18500/0869-6632-2009-17-2-66-86

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Controlling chaos in Ikeda system. Symplified discrete map model

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

Method of controlling chaos in a ring cavity containing a media with cubic phase nonlinearity (Ikeda system) is considered. The proposed method is based on introduction of an additional feedback loop with parameters chosen so that the fundamental frequency components after passing through different feedback loops appear in phase, while the most unstable sidebands appear in antiphase, thus suppressing each other. In the weak dispersion limit a discrete map is derived that is a modification of the well-known Ikeda map. The results of analytic investigation and numerical simulation of this map in a broad range of parameters are presented. It is shown that the suggested method allows suppression of self-modulation and stabilization of periodic regimes.

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