Noise-aided control of chaotic dynamics in a logistic map

Controlling chaos involves employing small perturbations to a control parameter, resulting in the stabilization of the system (naturally chaotic) on one of the infinite unstable periodic orbits embedded in the chaotic attractor. In this Brief Report we study the constructive role of external noise in increasing the efficiency of controlling chaos. Using a logistic map as an example, control of chaotic dynamics is achieved using a linear delayed-feedback strategy. Working in the subthreshold regime of control (where the value of control constant is less than the minimum value required to stabilize the period-1 target state), system dynamics in the presence of superimposed noise (system plus control plus noise) exhibit a resonance effect. Furthermore it is observed that the time required to reach the target state decreases appreciably in the presence of an optimum level of noise.