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.
Highlights
Chaos synchronization refers to a process wherein two dynamical systems adjust their motion to achieve a common behavior, mainly due to a coupling or control input [1]
The full-state hybrid projective synchronization (FSHPS) has been introduced, wherein each slave system variable synchronizes with a linear combination of master system variables
On the other hand, when the inverted scheme is implemented, i.e., each master system state synchronizes with a linear combination of slave system states, the inverse full-state hybrid projective synchronization (IFSHPS) is obtained [6]
Summary
Chaos synchronization refers to a process wherein two dynamical systems (master and slave systems, respectively) adjust their motion to achieve a common behavior, mainly due to a coupling or control input [1]. Projective synchronization provides the slave system variables consisting in scaled replicas of the master system variables [5]. The full-state hybrid projective synchronization (FSHPS) has been introduced, wherein each slave system variable synchronizes with a linear combination of master system variables. On the other hand, when the inverted scheme is implemented, i.e., each master system state synchronizes with a linear combination of slave system states, the inverse full-state hybrid projective synchronization (IFSHPS) is obtained [6]. When the scaling factors are replaced by scaling functions, function-based hybrid synchronization schemes are obtained, i.e., the full-state hybrid function projective synchronization
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