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Advisor(s)
Abstract(s)
We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.
Description
Keywords
Couplings of chaotic dynamical systems Complete synchronization Delayed synchronization Windows of synchronization
Citation
LOPES, Luís Mário Monteiro; FERNANDES, Sara; GRÁCIO, Clara - Complete synchronization and delayed synchronization in couplings. Nonlinear Dynamics. ISSN 0924-090X. Vol. 79, N.º 2 (2015), pp. 1615-1624
Publisher
Springer