Particular attention is being paid these days to the mathematical modelling of the social behaviour of individuals in a biological population, for different reasons; on one hand there is an intrinsic interest in population dynamics of herds, on the other hand agent based models are being used in complex optimization problems (ACO’s, i.e. Ant Colony Optimization). Further decentralized/parallel computing is exploiting the capabilities of discretization of nonlinear reaction-diffusion systems by means of stochastic interacting particle systems.
These systems lead to selforganization phenomena exhibiting interesting spatial patterns.
As an example, here an interacting particle system modelling the social behaviour of ants is proposed, based on a system of stochastic differential equations, driven by social aggregating/repelling “forces” .
Specific reference to the species “Polyergus Rufescens” will be made, that has been observed in nature.
Extensions to models of chemotaxis, such as angiogenesis related to tumor growth, will be presented, in which the so called organization process is driven by an underlying field strongly coupled with the spatial structure of the population of interacting individuals/agents/cells.
Suitable “laws of large numbers” are shown to imply convergence of the empirical spatial distributions of interacting individuals to nonlinear reaction-diffusion equations, as the total number of individuals becomes sufficiently large.
A variety of model and parameter identification problems arise in this framework, for which the authors call for a possible solution.
Copyright. All Rights Reserved.