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

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.

Automated summary

This paper introduces a four-dimensional fractional-order chaotic system with cross-product nonlinearities. The stability of the equilibrium points is analyzed and feedback control design is implemented to achieve this goal. Furthermore, various dynamical behaviors such as phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. The global Mittag-Leffler attractive sets and Mittag-Leffler positive invariant sets of the considered fractional order system are also discussed. Numerical simulations are provided to demonstrate the effectiveness of the results.