Dominance of Milnor Attractors and Noise-Induced Selection in a Multiattractor System

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Abstract
In a multiattractor state of a globally coupled dynamical system, stability of the attractors is studied by recording the return rates to themselves after perturbations. Besides the basin volume, attractors are characterized by strength, defined as the threshold perturbation for the full return rate. It is observed that Milnor attractors with a vanishing strength are dominant in the partially ordered phase. Attractions to weak attractors are found to be often enhanced with the addition of a noise, selectively for its amplitude.