Dynamical systems with time-delayed interactions can synchronize on a common chaotic trajectory. For large delays the occurrence of synchronization depends on two key features: 1) The dynamical properties of the individual units of the network. One can distinguish between strong chaos and weak chaos, which is reflected in the scaling behavior of the maximum Lyapunov exponent with the delay time. Synchronization between strongly chaotic units is excluded, whereas in weak chaos synchronization is in principle possible. 2) The coupling topology. In a network of weakly chaotic systems one can predict the patterns of synchronization, using only the maximum Lyapunov exponent of each single unit and the eigenvalues of the adjacency matrix which describes the network. The analytical results on both aspects are exemplified by numerical simulations of the Lang-Kobayashi model for semiconductor lasers.
Reference: Phys. Rev. Lett. 107, 234102 (2011)
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