Dynamics of a class of fractional-order nonautonomous Lorenz-type systems.

The dynamical properties of a class of fractional-order Lorenz-type systems with quasi-periodic time-varying parameters are studied, where the fractional derivative is defined in the sense of Caputo. The effective non-integer dimension β is the sum of all the fractional orders. Deferring from the fractional-order autonomous Lorenz systems, the present nonautonomous systems have two critical values, β* and β*, of the effective non-integer dimension, 0<β*<β*<3, under which there exist a transition from chaos to quasi-periodic dynamics for some β near β* and a transition from quasi-periodic motion to regular dynamics (diverging to infinity) for some β near β*. The 0-1 test is applied to verify the existence of such strange dynamics.