Electron. J. Differential Equations, Vol. 2017 (2017), No. 128, pp. 1-15.

Coexistence of some chaos synchronization types in fractional-order differential equations

Adel Ouannas, Salem Abdelmalek, Samir Bendoukha

Referring to incommensurate and commensurate fractional systems, this article presents a new approach to investigate the coexistence of some synchronization types between non-identical systems characterized by different dimensions and different orders. In particular, the paper shows that complete synchronization (CS), anti-synchronization (AS) and inverse full state hybrid function projective synchronization (IFSHFPS) coexist when synchronizing a three-dimensional master system with a four-dimensional slave system. The approach is based on two new results involving stability theory of linear fractional systems and the fractional Lyapunov method. A number of examples are provided to highlight the applicability of the method.

Submitted March 10, 2017. Published May 10, 2017.
Math Subject Classifications: 34A08, 34H10, 34D06.
Key Words: Chaos synchronization; fractional-order systems; coexistence; fractional Lyapunov approach.

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Adel Ouannas
Laboratory of Mathematics
Informatics and Systems (LAMIS)
University of Larbi Tebessi
Tebessa, 12002 Algeria
email: ouannas.a@yahoo.com
Salem Abdelmalek
Department of mathematics
University of Tebessa, 12002 Algeria
email: sallllm@gmail.com
Samir Bendoukha
Electrical Engineering Department
College of Engineering at Yanbu
Taibah University, Saudi Arabia
email: sbendoukha@taibahu.edu.sa

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