# zbMATH — the first resource for mathematics

Dynamics of a class of fractional-order nonautonomous Lorenz-type systems. (English) Zbl 1387.37028
Summary: 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 $$\beta$$ is the sum of all the fractional orders. Deferring from the fractional-order autonomous Lorenz systems, the present nonautonomous systems have two critical values, $$\beta_*$$ and $$\beta^*$$, of the effective non-integer dimension, $$0 < \beta_* < \beta^* < 3$$, under which there exist a transition from chaos to quasi-periodic dynamics for some $$\beta$$ near $$\beta^*$$ and a transition from quasi-periodic motion to regular dynamics (diverging to infinity) for some $$\beta$$ near $$\beta_*$$. The 0-1 test is applied to verify the existence of such strange dynamics.{