STABILITY OF AN AUTOCATALYTIC SYSTEM UNDER NOISE PERTURBATIONS AND ITS DEPENDENCE ON THE BASIN OF ATTRACTION

The stability of an autocatalytic system subject to noise perturbation s is investigated. It is found that for non-fractal basins, noise alwa ys induces a transition from the stable focus to the stable node in th e system. A critical amplitude is defined as the minimum standard devi ation in Gaussian-distributed noise required to induce a transition in a prescribed interval of time. For non-fractal basins, the logarithm of the critical amplitude depends linearly on the area of the basin of attraction. As the bifurcation parameter approaches the interval corr esponding to chaotic behaviour, a marked deviation from linear depende nce is observed. Subsequent to the emergence of chaotic dynamics, the basin of attraction becomes fractal. On changing from a non-fractal to a fractal basin by a continuous change in the bifurcation parameter, the critical amplitude is discontinuously reduced. From these results, it is concluded that the basin of attraction of a dynamical state, ra ther than the dynamical patterns of that state, determines its stabili ty.