Mathematical modeling and Ada simulation of some synchronization processes

Abstract

Previously, a simulation model was proposed for the purpose of investigating synchronization, a phenomenon which is demonstrated in the well-known Rope Game (or Tug-of-War). Synchronous activity is evident in so-called self-organizing systems, particularly muscle and brain tissues. This paper gives an exact matrix description of the rope model and shows that study of the synchronous behavior of this model can be done by applying Markov chain analysis. In modeling neural networks, however, such features as refraction, inhibition, noise, and discrete neuron responses frequently are incorporated in simulation models. Simulations are presented that indicate certain neural network models can be more simply modeled in part using a matrix representation similar to that for the rope game. A lemma is proved and used to obtain a formula for neuron firing expected in steady state.