Comparative Analysis of the Chaotic Behavior of a Five-Dimensional Fractional Hyperchaotic System with Constant and Variable Order

Abstract

A five-dimensional hyperchaotic system is a dynamical system with five state variables that exhibits chaotic behavior in multiple directions. In this work, we incorporated a 5D hyperchaotic system with constant- and variable-order Caputo and the Caputo–Fabrizio fractional derivatives. These fractional 5D hyperchaotic systems are solved numerically. Through simulations, the chaotic behavior of these fractional-order hyperchaotic systems is analyzed and a comparison between constant- and variable-order fractional hyperchaotic systems is presented.

Keywords

• fractional derivative with constant order
• fractional derivative with variable order
• hyperchaotic system
• numerical solutions
• simulations