The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control

Abstract

The dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C0 complexity, and algorithm 0–1 are presented in detail in this article. The efficiency of these algorithms in the existence of chaos for FO systems has been investigated as well as other methods such as Lyapunov exponents, Lyapunov dimension, and bifurcation diagrams. With Hamilton’s energy analysis for the 4D FO system, it is found that chaotic behavior is more dependent on energy consumption. Therefore, it is necessary to design a negative feedback control to reduce energy consumption and suppress chaotic behavior. Finally, we obtain the global Mittag-Leffler positive invariant sets (GMLPISs) and global Mittag-Leffler attractive sets (GMLASs) of the introduced system. Numerical results indicate the effectiveness of complexity and chaos detection methods as well as bound calculation.

Keywords

• Complexities
• Hamilton energy function (HEF)
• Fractional-order
• Energy control