Probabilistic control of chaos through small perturbations

We study the method of probabilistic control of chaotic dynamics (I. Antoniou, V. Basios, F. Bosco, Int. J. Bif., Chaos 6 (1996) 1563; I. Antoniou, V. Basios, F. Bosco, Absolute controllability condition for probablistic control of Chaos, Int. J. Bif., Chaos 8(2) (1998) 409) in connection with small random perturbations of the map parameter. By constructing a probabilistic dynamical system equivalent to the perturbed chaotic map we calculate a characteristic exponent which gives controllability conditions in terms of the applied perturbations.