Synchronization of N-coupled incommensurate fractional-order chaotic systems with ring connection

In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to synchronize N-coupled incommensurate fractional-order chaotic systems with ring connection. Chaos synchronization is studied by utilizing the coupling method that includes unidirectional and bidirectional coupling. The main contribution of this work is to design the coupling parameters in which it is shown that our proposed controller does stabilize error dynamics around all of equilibriums of master system. Finally, the claims are justified through a set of simulations and results coincide with the theoretical analysis.

Research highlights
► There are different connections between N-coupled chaotic systems such as the ring connection, star connection and so on that the first has been considered in our paper.
► In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to synchronize N-coupled incommensurate fractional-order chaotic systems with ring connection.
► Chaos synchronization has been studied by utilizing the coupling method that includes unidirectional and bidirectional coupling.
► The main contribution of this work is to design the coupling parameters in which it is shown that our proposed controller does stabilize error dynamics around all of equilibriums of master system.
► Finally, the claims are justified through a set of simulations and results coincide with the theoretical analysis.