Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

Abstract

In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. Finally, the global Mittag–Leffler attractive sets (MLASs) and Mittag–Leffler positive invariant sets (MLPISs) of the considered fractional order system are presented. Numerical simulations are provided to show the effectiveness of the results.

Keywords

• fractional-order hyperchaotic system
• global Mittag–Leffler attractive sets (MLASs)
• Mittag–Leffler positive invariant sets (MLPISs)
• chaos control