Formal Validation of Asynchronous Interaction-Agents Algorithms for Reaction-Diffusion Problems

In the context of biological complex systems multi-agent simulation, we present an interaction-agent model for reaction-diffusion problems that enables interaction with the simulation during the execution, and we establish a mathematical validation for our model. We use two types of interaction-agents: on one hand, in a chemical reactor with no spatial dimension -e.g. a cell-, a reaction-agent represents an autonomous chemical reaction between several reactants, and modifies the concentration of reaction products. On the other hand, we use interface-agents in order to take into account the spatial dimension that appears with diffusion : interface-agents achieve the matching transfer of reactants between cells. This approach, where the simulation engine makes agents intervene in a chaotic and asynchronous way, is an alternative to the classical model - which is not relevant when the limits conditions are frequently modified- based on partial derivative equations. We enounciate convergence results for our interaction-agent methods, and illustrate our model with an example about coagulation inside a blood vessel.