Chaotic Dynamics of Tempered Fractional Lorenz System and Its Synchronization

Based on tempered fractional derivatives, in this paper, the prediction-corrector scheme of tempered fractional differential equation is studied by using the characteristics of chaotic systems, and it is used to simulate the chaotic behaviors of tempered fractional Lorenz systems. The method works well for tempered fractional differential equation of arbitrary order. A striking finding of the simulation is that the dynamical behaviors of tempered fractional Lorenz system become stronger as
$\lambda(\lambda$
is a temper parameter) decreases. Finally, the synchronization of the classical Lorenz systems and tempered fractional Lorenz systems is discussed.