Are Some Voltage State Orbits, Computed in a Discrete-Time Hopfield Neural Network, Which Correspond to Bifurcation Values, Fractals? Exists these Orbits in Reality or they Exists Just in Theory i.e. has these Orbits a Real Counterpart?

Abstract

Andreea V. Cojocaru and Stefan Balint

In case of a discrete-time Hopfield neural network of two neurons with two delays and no self-connections at 20 bifurcation values 20 voltage trajectories appear. Among the 20 voltage trajectories 14 voltage trajectory are not what we call orbits in classic sense. The geometrical aspect of these trajectories suggest that they are fractals. Our conjecture is that the 14 trajectories in discussion are fractals having real counterpart. In case of a discrete-time Hopfield neural network of five neuron with delay and ring architecture at 9 bifurcation values 9 voltage trajectories appear. Among the 9 voltage trajectories we find 5 voltage trajectory which are not what we call orbits in classic sense. The geometrical aspect of these trajectories suggest that they are fractals. Our conjecture is that the 5 trajectories in discussion are fractals having real counterparts.. In case of a discrete-time, Hopfield neural network of two neurons with a single delay and self- connections the computed trajectories are what we call orbits in classic sense. In case of a discrete-time, Hopfield neural network of two neurons with two delays and self- connections the computed trajectories are what we call orbits in classic sense.

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