Dynamics, circuit implementation and synchronization of a new three-dimensional fractional-order chaotic system

In this paper, a new three-dimensional autonomous fractional-order chaotic system is presented. There are four different nonlinear terms in the governed equations. By means of theoretical analysis and numerical simulation, some basic dynamical properties, such as phase diagrams, bifurcation diagram, Lyapunov exponents spectrum and chaos diagram of the new fractional-order chaotic system are investigated. Then, we completed the circuit design of the fractional-order chaotic system, and realized the analog hardware circuit. Both the hardware experiment results and circuit simulation results are agreed well with those of numerical simulation. Finally, based on the theory of sliding-mode control and the fractional stability theory, a suitable sliding mode controller is designed for the novel three-dimensional fractional-order chaotic system. Numerical simulations are provided to verify the effectiveness of the proposed synchronization scheme.