Synchronization of Chaos - Anticipated and Lag Synchronization

Anticipated and Lag Synchronization

In these cases the synchronized state is characterized by a time interval τ such that the dynamical variables of the oscillators, (x₁,x₂,,...,x_n) and (x'₁, x'₂,...,x'_n), are related by x'_i(t)=x_i(t+τ); this means that the dynamics of one of the oscillators follows, or anticipates, the dynamics of the other. Anticipated synchronization may occur between chaotic oscillators whose dynamics is described by delay differential equations, coupled in a drive-response configuration. In this case, the response anticipates the dynamics of the drive. Lag synchronization may occur when the strength of the coupling between phase-synchronized oscillators is increased.