A Mathematical Formalism of Hierarchical Systems for a Distributed Simulation: Case of the Nervous System

In this paper we present a mathematical formulation of hierarchical systems based on graphs. In particular we are interested in the mathematical theory of integrative physiology (MTIP) developed by Gilbert Chauvet, which describes biological structures and their functioning as a combination of hierarchical structures (synapses, neurones, neural network) and of functional interactions between these structures. In this work our aim is to provide a mathematical modeling of the nervous system as a hierarchical network using pretopology theory in the framework of the MTIP.