Citation:
Ouannas A, Abdelmalek S, Bendoukha S. Coexistence of some chaos synchronization types in fractional-order differential equations. Electronic Journal of Differential Equations [Internet]. 2017;128 :1-15.
Abstract:
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.