Circuit Implementations, Bifurcations and Chaos of a Novel Fractional-Order Dynamical System

Linear transfer function approximations of the fractional integrators 1/s^m with m=0.80–0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency?domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1/s^m with a slope of -20m dB/decade are depicted. By using the transfer function approximations of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.