Chaos and chaos control in MEMS resonators under power law noise

The chaotic dynamics and its control under power law noise in Micro-electromechanical Systems (MEMS) resonators with electrostatic excitation are probed. On the basis of the stochastic Melnikov method in the mean-square sense and the mean largest Lyapunov exponent, the threshold value of power law noise intensity for the onset of chaos is obtained analytically and numerically. We show that the threshold of noise intensity decreases with the increasing of the frequency exponent of power law noise in the parameter space. Numerical simulations, such as phase diagram and time history, are employed to verify the results acquired by the stochastic Melnikov method. Inspired by the analytical results, a time-delay feedback control algorithm is proposed for controlling the chaotic motion in the resonators. The effectiveness of this controller is certificated by the above numerical method.