Impact of Fractional Orders on Characteristics of Chaotic Dynamical Systems
Chaotic control of dynamical systems has become a subject with intense interests in science and engineering. Chaotic behaviors of dynamical systems could be highly sensitive to initial conditions, which has been widely recognized and examined, such as the butterfly effect. The chaotic attribute will take place on an attractor while the fractal structure will further contribute to the formulation of strange attractors. However, the fractional order analysis of typical chaotic systems has not been thoroughly conducted in literatures. Qualitative analysis of fractional orders on chaotic system characteristics is thus made, which provides a useful basis for applying fractional order control to generate or suppress the chaotic behaviors exhibited in diverse engineering systems. Global stability ranges of two typical fractional order dynamical systems are reached via observations. Synchronization and fractional order control approaches are also proposed.
Index Terms — Chaos, Lorenz Dynamical System, Chua Dynamical System, Synchronization, Fractional Order Control