SYNCHRONIZATION OF CHAOTIC ORBITS - THE EFFECT OF A FINITE-TIME STEP

Two chaotic orbits can be synchronized by driving one of them by the o ther. Some of the variables of the driven orbit are set continuously t o the corresponding variables of the drive orbit. It has been seen tha t synchronization can be achieved if the subsystem Lyapunov exponents corresponding to the remaining or response variables are all negative. We find that a procedure where the drive variable is set at discrete times can also achieve synchronization. However, the synchronization c riterion is altered by the effect of the drive being set at finite tim e steps. An important consequence of this is found in the Lorenz syste m where synchronization can be achieved with z as the drive variable d espite the existence of a marginal subsystem Lyapunov exponent. We als o find that synchronization can be achieved for the Rossler attractor with z as the drive, even though the largest subsystem Lyapunov expone nt is positive. In addition, we find that there is an optimal time ste p corresponding to the fastest rate of convergence for both cases abov e. Our synchronization criterion reduces to the usual subsystem-Lyapun ov-exponent criterion in the limit of the time step tending to zero.