Quaternion anti-synchronization of a novel realizable fractional chaotic model. (March 2021)

• Record Type: Journal Article
• Authors: Mahmoud, Emad E.; Higazy, M.; Alotaibi, Hammad; Abo-Dahab, S.M.; Abdel-Khalek, S.; Khalil, E.M.
• Is Part Of: Chaos, solitons and fractals. Volume 144(2021)
• Publication Date: 2021-03
• Subjects: Fractional order chaotic systems -- Signal flow graphs -- Electronic circuit realization -- Quaternion variables -- Quaternion anti synchronization -- Fractional derivative; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.110715
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Using the quaternion mathematics and fractional derivative, the unified chaotic system is generalized. A novel 8.1-fractional-order quaternion 9Ds unified chaotic system is constructed and its dynamics are studied. The novel 8.1-fractional-order quaternion 9Ds unified chaotic system is realized by tree shape electronic circuit. A novel quaternion anti-synchronization (QAS) technique is proposed and discussed. The QAS technique is applied to a pair of the novel 8.1-fractional-order quaternion 9D unified chaotic system. Abstract: The main aim of this work is to generalize the chaotic unified model using the quaternion mathematics and fractional derivatives. A novel 8.1-fractional order, 9-dimensions, quaternion unified chaotic system is constructed. The 8.1-fractional order electronic circuit that realize the novel system is designed. Using the graph theory tools, the complexity of the proposed novel 8.1-fractional order, 9-dimensions, quaternion unified chaotic system is calculated. In addition, the substantial contribution in this work appears in introducing an extraordinary type of quaternion synchronizations. We call this novel type "quaternion anti synchronization" (QAS). QAS has unusual properties and characteristics that distinguish it from all the types of synchronizations previously studied in the literature. The QAS of fractional unified model with quaternion variables is studied. The validity of the analytical results is confirmed in QAS of fractional unified system with effective numerical simulation.