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Abstract: We report the identification of global phase synchronization GPS in alinear array of unidirectionally coupled Mackey-Glass time-delay systemsexhibiting highly non-phase-coherent chaotic attractors with complextopological structure. In particular, we show that the dynamical organizationof all the coupled time-delay systems in the array to form GPS is achieved bysequential synchronization as a function of the coupling strength. Further, theasynchronous ones in the array with respect to the main sequentiallysynchronized cluster organize themselves to form clusters before they achievesynchronization with the main cluster. We have confirmed these results byestimating instantaneous phases including phase difference, average phase,average frequency, frequency ratio and their differences from suitablytransformed phase coherent attractors after using a nonlinear transformation ofthe original non-phase-coherent attractors. The results are furthercorroborated using two other independent approaches based on recurrenceanalysis and the concept of localized sets from the original non-phase-coherentattractors directly without explicitly introducing the measure of phase.



Autor: R. Suresh, D. V. Senthilkumar, M. Lakshmanan, J. Kurths

Fuente: https://arxiv.org/



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