Dynamical Hysteresis Neural Networks for Graph Coloring Problem

Abstract

We analyze syncronization phenomena in a dynamical hysteresis neural network. The dynamical hysteresis neural network accounts a phase differece in each neuron to be an information. Based on this result, we propose an application for solving 2-colorable graph coloring problems. A system that can treat dynamical information, is attracted to great attention. The reason why such system receives great attention, is that dynamical information processing functions can be found in biological neural networks. Especially, we think that a synchronization phenomenon plays an important role for signal processing in the brain. Our system consists of relaxation oscillators in which contain hysteresis elements. The relaxation oscillator is regarded as a multi-vibrator, namely, the system takes bistable, monostable, and astable state. By using stable and monostable state, we proposed a combinatorial optimization solver that its stable equilibrium point is regarded as an information. On the other hand, various kinds of attractors exist in the hysteresis neural network. We consider that periodic and aperiodic attractors have rich information. For exploiting such attractors, we proposed a novel dynamical associative memory whose information is represented by phase difference. This behavior relates synchronization phenomena. In this article, we will analyze synchronization phenomena in a coupled hysteresis neuron. And, we will propose an application which can dye 2-colorable graph.