On the Strength of Attractors in a High-dimensional System: Milnor Attractor Network, Robust Global Attraction, and Noise-induced Selection

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.