Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

Abstract

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

“…Elvakil et al 38 took into account a double wing attractor and found a case of mirror plane symmetric chaotic attractor in a modified Lorenz system. New techniques for producing multi-scroll attractors have been developed since this work was published 39 – 41 . For the past decade, scientists have experimented with various signal functions, such as switching control 42 , piece-wise hysteresis function 43 , shifting transformation 44 , saw−tooth function 45 , 46 and train pulses 47 , to generate multiple scrolls.…”