Generalized synchronization and complexity in unidirectionally coupled dynamical systems

概要

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We investigate generalized synchronization and complexity in unidirectionally coupled Rössler systems and Mackey-Glass systems with time-delayed feedback. The generalized synchronization is measured by using two identical response systems which are driven by a common drive system. To measure the complexity, KS entropy and KY dimension are calculated quantitatively from the Lyapunov spectrum by using the linearized equations. The response systems show generalized synchronization for large coupling strengths. The entropy and dimensionality decrease as the coupling strength is increased. The minimum value of entropy is obtained at the condition of generalized synchronization, whose value corresponds to the entropy for the solitary drive system, even though the temporal waveforms of the drive and response systems are significantly different. The maximum entropy is achieved outside the region where generalized synchronization is achieved, whose value almost corresponds to the sum of those of the two solitary drive and response systems. It is found that the coupling effect changes the entropy within these two values. The dimensionality decreases monotonically even within the region of generalized synchronization.