Phase transitions in a probabilistic cellular neural network model having local and remote connections

Inspired by a neuronal architecture, we show how to produce dynamical behaviors in a special kind of probabilistic cellular neural network system. We demonstrate that the spatial and temporal behavior of neural activity undergoes sudden changes if the connection structure and noise component are varied. We characterize quantitatively phase transitions using the activation and cluster size. We indicate the potential role our present results may play in developing the theory of computation using non-convergent neurodynamic principles, called neurpercolation.

I. INTRODUCTION

Methods of multi-component stochastic systems theory are applied in many parts of biology on the molecular, cellular, genetic, and population levels; in computer science; in polymer chemistry; in seismology; in economics, and other sciences. From the probabilistic point of view, such systems are special cases of multidimensional Markov processes [1]. Two main principles are applied. The systems are treated as multi-component and homogeneous, i.e. all components have similar rules of behavior. Systems like these can be used to describe central nervous system functioning [2], [3].