Abstract:
Through a series of non-singular linear transformation and Laplace transformation, and with help of properties of the convergence and divergence of special function Mittag-Leffler function, the dynamic behavior of Caputo type fractional-order autonomous system of three-dimension in phase space were studied comprehensively and deeply for the first time. The variation cases of equilibrium points with parameters and the dynamic behaviors of line in the neighborhood of equilibrium points in phase space were further analyzed. Finally, the graphic maps of the orbit distribution of the system were given overall. The research results show that there is neither a central equilibrium point nor a closed orbit in the Caputo type fractional-order three-dimensional dynamic system, thus there is no corresponding periodic solution, which provides a new example for the fractional-order linear differential equations without periodic solution.