Lyapunov Functionals Associated to Neural Network
In Chapter 2 we analized the steady state behavior of Neural and Majority Networks by means of algebraic invariants which enabled the characterization of periods. Unfortunately, the transient behavior does not yield as readily to a study based on such class of invariants. To overcome the difficulty, we introduce here Lyapunov functionals driving the network dynamics. Using this kind of functionals, explicit bounds to the transient length will be found. Moreover, Lyapunov functionals provide a physical interpretation of Neural Networks. These operators were first introduced by Hopfield [Ho2] to analize the fixed point behaviour of random sequential iterations of associative networks. As for their application in the study of synchronous updating rules and of memory updating, they were defined and developed in [G2,GFP]. Besides, they were applied to a reversible automaton in [Po].
KeywordsNeural Network Symmetric Matrix Sequential Iteration Integer Matrix Real Symmetric Matrix
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