SYNCHRONIZATION INDUCED BY INTERMITTENT VERSUS PARTIAL DRIVES IN CHAOTIC SYSTEMS

We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization behavior of both systems can be inferred by considering the dynamics of a single chaotic map driven with a probability p. The synchronized states for these systems are characterized on their common space of parameters. Our results show that the presence of a common external drive for all times is not essential for reaching synchronization in a system of chaotic oscillators, nor is the simultaneous sharing of the drive by all the elements in the system. Rather, a crucial condition for achieving synchronization is the sharing of some minimal, average information by the elements in the system over long times. PACS numbers: 05.45.-a, 05.45.Xt, 05.45.Ra Chaos synchronization has attracted much interest from both scientists and engineers by providing insights into natural phenomena and motivation for practical applications in communications and control [Pecora & Carroll, 1990; Boccaletti et al., 2002; Uchida et al., 2005; Argyris et al., 2005; Pikovsky et al., 2002]. This phenomenon is commonly observed in unidirectionally coupled systems, where a distinction can be made between a drive or forcing subsystem and another driven or response subsystem that possesses chaotic dynamics [Pikovsky et al., 2002]. Complete synchronization occurs when the state variables of the driving and the response subsystems converge to a single trajectory in phase space. On the other hand, generalized synchronization of chaos arises when a functional relation different from the identity is established between the drive and the response subsystem