Concept of Q-S synchronization for fractional-order systems is introduced and Q-S synchronization of the fractional-order unified system is investigated in this paper. On the basis of the stability theory of the fractional-order system, two suitable control schemes are designed to achieve Q-S synchronization of the fractional-order unified systems under the given observable variables of drive system and the response system. Theoretical analysis and numerical simulations are shown to demonstrate the validity and feasibility of the proposed method.

Dynamics of fractional-order memristor circuit system and its control are investigated in this paper. With the help of stability theory of fractional-order systems, stability of its equilibrium points is analysed. Then, the chaotic behaviours are validated using phase portraits, the Lyapunov exponents and bifurcation diagrams with varying parameters. Furthermore, some conditions ensuring Hopf bifurcation with varying fractional orders and parameters are determined, respectively. By using a stabilization theorem proposed newly for a class of nonlinear systems, linear feedback controller is designed to stabilize the fractional-order system and the corresponding stabilization criterion is presented. Numerical simulations are given to illustrate and verify the effectiveness of our analysis results.