Electronic Journal of Differential Equations (May 2017)

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

  • Adel Ouannas,
  • Salem Abdelmalek,
  • Samir Bendoukha

Journal volume & issue
Vol. 2017, no. 128,
pp. 1 – 15

Abstract

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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.

Keywords