A continuous Hopfield network equilibrium points algorithm

The continuous Hopfield network (CHN) is a classical neural network model. It can be used to solve some classification and optimization problems in the sense that the equilibrium points of a differential equation system associated to the CHN is the solution to those problems. The Euler method is the most widespread algorithm to obtain these CHN equilibrium points, since it is the simplest and quickest method to simulate complex differential equation systems. However, this method is highly sensitive with respect to initial conditions and it requires a lot of CPU time for medium or greater size CHN instances. In order to avoid these shortcomings, a new algorithm which obtains one equilibrium point for the CHN is introduced in this paper. It is a variable time-step method with the property that the convergence time is shortened; moreover, its robustness with respect to initial conditions will be proven and some computational experiences will be shown in order to compare it with the Euler method.