Controlling chaos

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 Schr¨ odinger 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].

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.