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

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2 Author(s)
Cohen, M.A. ; Dept. of Math., Boston Univ., Boston, MA, USA ; Grossberg, S.

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.

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Systems, Man and Cybernetics, IEEE Transactions on  (Volume:SMC-13 ,  Issue: 5 )