Controlling chaos by bounded self-controlling function using Butterworth filter feedback

Using the bounded sigmoid function and two-order Butterworth low-pass filter, a self-controlling feedback method for regulate the motion of a chaotic system is presented in this paper. It is shown that such controller has the advantage of being easy to implement based on the measurable input signals. A rigorous stability proof is provided from LaSalle Invariance theorem. Furthermore, the effectiveness and efficiency of the proposed feedback control strategy is illustrated by means of the numerical simulations of two-well Duffing Vander Pol oscillator. Finally, the result reveals that the enough large maximum amplitude results in a more possible regular domain in parameter space of the controlled oscillator.