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The chaotic dynamics and its control under power law noise inMicro-electromechanical Systems (MEMS) resonators with electrostatic excitationare probed. On the basis of the stochastic Melnikov method in the mean-squaresense and the mean largest Lyapunov exponent, the threshold value of power lawnoise intensity for the onset of chaos is obtained analytically andnumerically. We show that the threshold of noise intensity decreases with theincreasing of the frequency exponent of power law noise in the parameter space.Numerical simulations, such as phase diagram and time history, are employed toverify the results acquired by the stochastic Melnikov method. Inspired by theanalytical results, a time-delay feedback control algorithm is proposed forcontrolling the chaotic motion in the resonators. The effectiveness of thiscontroller is certificated by the above numerical method.

Chaos and chaos control in MEMS resonators under power law noise