Function-based hybrid synchronization types and their coexistence in non-identical fractional-order chaotic systems

Abstract

Abstract This paper presents new results related to the coexistence of function-based hybrid synchronization types between non-identical incommensurate fractional-order systems characterized by different dimensions and orders. Specifically, a new theorem is illustrated, which ensures the coexistence of the full-state hybrid function projective synchronization (FSHFPS) and the inverse full-state hybrid function projective synchronization (IFSHFPS) between wide classes of three-dimensional master systems and four-dimensional slave systems. In order to show the capability of the approach, a numerical example is reported, which illustrates the coexistence of FSHFPS and IFSHFPS between the incommensurate chaotic fractional-order unified system and the incommensurate hyperchaotic fractional-order Lorenz system.

Keywords

• Coexistence of synchronization types
• Full-state hybrid function projective synchronization
• Inverse full-state hybrid function projective synchronization
• Incommensurate fractional-order systems
• Non-identical systems