Hysteresis neural network for coloring graph problems using synchronization phenomena

摘要

Recently, an artificial neural network that can treat dynamical information, is attracted to great attention. The reason why such system receives great attention, is that dynamical information processing function can be found in biological neural networks. Especially, a synchronization phenomenon plays an important role for signal processing in the brain. In this report, we consider synchronization phenomena in a hysteresis neural network which contains piecewise-linear bipolar hysteresis elements. The hysteresis element is regarded as a multi-vibrator, namely, the system behaves bistable, monostable, and astable state. When all hysteresis elements take as table state, the system exhibits a synchronization phenomenon which is controlled by its connection coefficients. For exploiting such synchronization state, we propose a dynamical hysteresis neural network accounts a phase difference in each neuron to be an information. Also, we propose its application to solve graph coloring problems.