Derivation of a micro-macro link for collective decision-making systems uncover network features based on drift measurements

Abstract

Relating microscopic features (individual level) to macroscopic features (swarm level) of self-organizing collective systems is challenging. In this paper, we report the mathematical derivation of a macroscopic model starting from a microscopic one for the example of collective decision-making. The collective system is based on the application of a majority rule over groups of variable size which is modeled by chemical reactions (micro-model). From an approximated master equation we derive the drift term of a stochastic differential equation (macromodel) which is applied to predict the expected swarm behavior. We give a recursive definition of the polynomials defining this drift term. Our results are validated by Gillespie simulations and simulations of the locust alignment.