Absolute stability of global pattern formation and parallel memory storage by competitive neural networks

It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the LyAPunov functional approach, will ultimately handle all of the physically important cases.

Abstract

Systems that are competitive and possess symmetric interactions admit a global Lyapunov function. However, a global Lyapunov function whose equilibrium set can be effectively analyzed has not yet been discovered. It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the Lyapunov functional approach, which sidesteps a direct study of equilibrium points will ultimately handle all of the physically important cases.