A fractional-order brushless DC motor (BLDCM) system is proposed in this paper. By computer simulations, we find that the fractional-order BLDCM system exhibits a chaotic attractor for fractional order 0.96 < q ≤ 1, and that the largest Lyapunov exponent varies depending on fractional-order q. Furthermore, in order to stabilize the fractionalorder chaotic BLDCM system, two control strategies are presented via single input, based on the generalized Gronwall inequality and the Mittag-Leffler function. Numerical simulations are presented to verify the validity and feasibility of the proposed control schemes.

Based on a special matrix structure, the projective synchronization control laws of the hyperchaotic financial systems are proposed in this paper. Put a hyperchaotic financial system as the drive system, via transformation of the system state variables, construct its response system, and then design the controller based on the special matrix structure. The given scheme is applied to achieve projective synchronization of the different hyperchaotic financial systems. Numerical experiments demonstrate the effectiveness of the method.

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