Targeting fixed-point solutions in nonlinear oscillators through linear augmentation

We propose a general strategy to stabilize the fixed points of nonlinear oscillators with augmented dynamics. By using this scheme, either the unstable fixed points of the oscillatory system or a new fixed point of the augmented system can be stabilized. The Lyapunov exponents are used to study the dynamical properties. This scheme is illustrated with a chaotic Lorenz oscillator coupled through an external linear dynamical system. The experimental demonstration of the proposed scheme to stabilize the fixed points is also presented.