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