Control and Synchronization of Chaotic Systems in Dimension 3 or More

Abstract

In this work we studied the control and the synchronization of the chaotic systems of fractional order. We presented a new fractional system which based on the definition of the Caputo derivative and which displays a chaotic behavior from a specific value of commensurable minimum order, in which the theoretical and numerical solution representation of this system is given using the Adams-Bashforth-Moulton algorithm which uses to solve fractional order systems numerically. Also the full hybrid projective synchronization of state (FSHPS) is studied between the new 3D chaotic fractional order system and the hyper-chaotic fractional order Lorenz system. The results show that FSHPS is successfully performed between the two systems, indicating that this method can be used to synchronize similar chaotic fractional-order systems in other applications.