Fractional-order Chua's circuit: Time-domain analysis, bifurcation, chaotic behavior and test for chaos

In this tutorial the chaotic behavior of the fractional-order Chua's circuit is investigated from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which enables the solution of the fractional differential equations to be found in closed form. By exploiting the capabilities offered by the decomposition method, the paper presents two remarkable findings. The first result is that a novel bifurcation parameter is identified, that is, the fractional-order q of the derivative. The second result is that chaos exists in the fractional Chua's circuit with order q = 1.05, which is the lowest order reported in literature for such circuits. Finally, a reliable and efficient binary test for chaos (called 0-1 test) is utilized to detect the presence of chaotic attractors in the system dynamics.