A Novel Fractional Chaotic System with the 3-scroll and 4-scroll Chaotic Attractors and Impact of Memory Effect

Abstract

In the last few decades, a fractional calculus in chaotic systems has been widely researched due to its delicacy in engineering applications. This research has proposed a novel fractional-order chaotic system with a multi-scroll chaotic attractor. The system can generate 3-scroll and 4-scroll chaotic attractors by only adjusting a fractional order. The mathematical model is described by using the Caputo derivative form. The basic dynamic is analyzed as a stability condition, Lyapunov exponent, Kaplan-Yorke dimension, etc. The memory effect is one of the unique properties of a fractional-order chaotic system. This research discussed the memory effect by using the Kernel function of Mittag-Leffler. The results reveal that the long-time simulation of the system affects the characteristic of chaotic behavior for 3-scroll and 4-scroll chaotic attractors due to the memory effect. It confirms that fractional-order systems exhibit inherent memory properties, which effectively enhance the accuracy of prediction and forecasting applications.