Dynamics of fractional-order sinusoidally forced simplified Lorenz system and its synchronization

In this paper, dynamical behaviors of the fractional-order sinusoidally forced simplified Lorenz are investigated by employing the time-domain solution algorithm of fractional-order calculus. The system parameters and the fractional derivative orders q are treated as bifurcation parameters. The range of the bifurcation parameters in which the system generates chaos is determined by bifurcation, phase portrait, and Poincaré section, and different bifurcation motions are visualized by virtue of a systematic numerical analysis. We find that the lowest order of this system to yield chaos is 3.903. Based on fractional-order stability theory, synchronization is achieved by using nonlinear feedback control method. Simulation results show the scheme is effective and a chaotic secure communication scheme is present based on this synchronization.