Analysis and circuit design of a fractional-order Lorenz system with different fractional orders

Abstract

The paper first discusses the recently reported fractional-order Lorenz system, analyzes it by using the frequency-domain approximation method and the time-domain approximation method, and finds its chaotic dynamics when the order of the fractional-order system varies from 2.8 to 2.9 in steps of 0.1. Especially for the fractional-order Lorenz system of the order as low as 2.9, the results obtained by the frequency-domain method are consistent with those obtained by the time-domain method. Some Lyapunov exponent diagrams, bifurcation diagrams, and phase orbits diagrams have also been shown to verify the chaotic dynamics of the fractional-order Lorenz system. Then, an analog circuit for the fractional-order Lorenz system of the order as low as 2.9 is designed to confirm its chaotic dynamic, the results from circuit experiment show that it is chaotic.