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Kerr oscillators are model systems which have practical applications innonlinear optics. Optical Kerr effect i.e. interaction of optical waves withnonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenonneeded to explain for example the process of light transmission in fibers andoptical couplers. In this paper we analyze the two Kerr oscillators coupler andwe show that there is a possibility to control the dynamics of this system,especially by switching its dynamics from periodic to chaotic motion and viceversa. Moreover the switching between two different stable periodic states isinvestigated. The stability of the system is described by the so-called maps ofLyapunov exponents in parametric spaces. Comparison of basins of attractionsbetween two Kerr couplers and a single Kerr system is also presented.

Periodic orbits, basins of attraction and chaotic beats in two coupled Kerr oscillators