  Strength of attractor is studied by the return rate to itself after
perturbations, for a multi-attractor state of a globally coupled map. It is
found that fragile (Milnor) attractors have a large basin volume at the
partially ordered phase. Such dominance of fragile attractors is understood by
robustness of global attraction in the phase space. Change of the attractor
strength and basin volume against the parameter and size are studied. In the
partially ordered phase, the dynamics is often described as Milnor attractor
network, which leads to a new interpretation of chaotic itinerancy.
Noise-induced selection of fragile attractors is found that has a sharp
dependence on the noise amplitude. Relevance of the observed results to neural
dynamics and cell differentiation is also discussed.
