New theorems on global convergence of some dynamical systems
Neural Networks
Neural techniques for combinatorial optimization with applications
IEEE Transactions on Neural Networks
Microcode optimization with neural networks
IEEE Transactions on Neural Networks
Design and analysis of maximum Hopfield networks
IEEE Transactions on Neural Networks
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A novel technique ispres ented that implementscon tinuousstate Hopfield neural networks on a digital computer. Instead of the usual forward Euler rule, the backward method is used. The stability and Lyapunov function of the proposed discrete model are indirectly guaranteed, even for reasonably large step size. This is possible because discretization by implicit numerical methodsinheritsthe stability of the continuoustime model. On the contrary, the forward Euler method requiresa very small step size to guarantee convergence to solutions. The presented technique takes advantage of the extensive research on continuous-time stability, asw ell asrecen t resultsin the field of dynamical analysisof numerical methods. Also, standard numerical methods allow for synchronous activation of neurons, thus leading to performance enhancement. Numerical results are presented that illustrate the validity of this approach when applied to optimization problems.