A stable attractor in chaos theory or biology is an equilibrium state into which a system settles until disrupted by a change in the environment. The system then settles to a new attractor.
In cellular automata a transition from a chaotic phase to a stable attractor is called a solution.
Some mathematical functions may never converge to a solution, but may cycle endlessly in a stable way.
Leibnitz et al. have devised a network routing scheme on a stable attractor model developed to account for the response of Escherichia coli bacteria to variations in nutrient availability. Information about data paths (bandwidth, transit time) is used to determine a stable attractor and to find a new attractor if the network falters. The system is stable in noisy environments[1].