Chaos in the discretized analog Hopfield neural network and potential applications to optimization

Abstract

We consider the discretization of the analog Hopfield neural network (DAHNN) using Euler approximation. We suggest an alternative approach to chaotic simulated annealing using the discretizing time-step Δt as the bifurcation parameter, because the DAHNN is chaotic when the time-step Δt is chosen to be sufficiently large and stabilization is guaranteed when the time-step Δt is small enough. It is not necessary to carefully choose other system parameters to assure minimization of Hopfield energy function and network convergence. We argue that this approach should find significant applications in solving combinatorial optimization problems with neural networks.