Dynamical Analysis of a One- and Two-Scroll Chaotic System

Abstract

In this paper, a three-dimensional (3D) autonomous chaotic system is introduced and analyzed. In the system, each equation contains a quadratic crossproduct. The system possesses a chaotic attractor with a large chaotic region. Importantly, the system can generate both one- and two-scroll chaotic attractors by choosing appropriate parameters. Some of its basic dynamical properties, such as the Lyapunov exponents, Lyapunov dimension, Poincaré maps, bifurcation diagram, and the chaotic dynamical behavior are studied by adjusting different parameters. Further, an equivalent electronic circuit for the proposed chaotic system is designed according to Kirchhoff’s Law, and a corresponding response electronic circuit is also designed for identifying the unknown parameters or monitoring the changes in the system parameters. Moreover, numerical simulations are presented to perform and complement the theoretical results.