Dynamics and synchronization of linearly coupled Kerr oscillators

The chaotical dynamics of two linearly coupled Kerr oscillators is studied. The system is damped and pumped by external time-dependent forces. The linearly coupled oscillators can behave in an orderly manner, chaotically or hyperchaotically according to the magnitude of the linear coupling, the frequencies of external forces and the loss mechanism. To indicate the type of attractor of the system we make use of Lyapunov exponents. Phase portraits of the system are presented. We show that the chaotic Kerr oscillators can be synchronized and the unidirectional and mutual synchronizations are studied.