Circuit Implementations, Bifurcations and Chaos of a Novel Fractional-Order Dynamical System**Supported by the National Natural Science Foundation of China under Grant No 51475246, the Natural Science Foundation of Jiangsu Province under Grant No Bk20131402, and the Ministry-of-Education Overseas Returnees Start-up Research Fund under Grant No [2012]1707.

Abstract

Linear transfer function approximations of the fractional integrators 1/sm 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/sm 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.