Capacity of an attractor to resist perturbations.
As stated By St KAUFFMAN: "Attractors tend strongly to exhibit homeostatic return after perturbation" (1993, p.209). However "The stability of an attractor is proportional to its basin size, which is the number of states on trajectories that drain into the attractor. Big attractors are stable to many perturbations, and small ones are generally unstable" (1991, p.67)
This explains the instability in chaotic systems, where frequent jumps occur between smaller and smaller attractors that appear through fractalizing bifurcations.
For the concept of "basin size" see "Basin of attraction"