Revealing Chaos Synchronization Below the Threshold in Coupled Mackey–Glass Systems

Marat Akhmet (), Kağan Başkan and Cihan Yeşil
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Marat Akhmet: Department of Mathematics, Middle East Technical University, Dumlupınar Boulevard, 06800 Ankara, Turkey
Kağan Başkan: Department of Physics, Middle East Technical University, Dumlupınar Boulevard, 06800 Ankara, Turkey
Cihan Yeşil: Department of Physics, Middle East Technical University, Dumlupınar Boulevard, 06800 Ankara, Turkey

Mathematics, 2023, vol. 11, issue 14, 1-15

Abstract: This study presents a novel concept in chaos synchronization, delta synchronization of chaos, which reveals the presence of chaotic models evolving in unison even in the absence of generalized synchronization. Building upon an analysis of unpredictability in Poincaré chaos, we apply this approach to unilaterally coupled time-delay Mackey–Glass models. The main novelty of our investigation lies in unveiling the synchronization phenomenon for a coupling constant below the synchronization threshold, an unattainable domain for conservative methods. Furthermore, we rigorously examine the coexistence of generalized synchronization and complete synchronization of unpredictability, which is a special case of delta synchronization, above the threshold. Therefore, the threshold is no longer a requirement for the synchronization of chaos in view of the present results. Additionally, transitions to fully chaotic regimes are demonstrated via return maps, phase portraits, and a bifurcation diagram. The findings are substantiated by tables and novel numerical characteristics.

Keywords: synchronization; delta synchronization; unpredictability; Poincaré chaos; Mackey–Glass system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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