Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System

Abstract

A novel nonlinear four-dimensional hyperchaotic system and its fractional-order form are presented. Some dynamical behaviors of this system are further investigated, including Poincaré mapping, parameter phase portraits, equilibrium points, bifurcations, and calculated Lyapunov exponents. A simple fourth-channel block circuit diagram is designed for generating strange attractors of this dynamical system. Specifically, a novel network module fractance is introduced to achieve fractional-order circuit diagram for hardware implementation of the fractional attractors of this nonlinear hyperchaotic system with order as low as 0.9. Observation results have been observed by using oscilloscope which demonstrate that the fractional-order nonlinear hyperchaotic attractors exist indeed in this new system