An equation-free approach to agent-based computation: Bifurcation analysis and control of stationary states

¹ School of Applied Mathematics and Physical Sciences, National Technical University of Athens Athens, GR 157 80, Greece, EU
² Department of Chemical and Biological Engineering, Princeton University - Princeton, 08544, NJ, USA

^(a) yannis@princeton.edu

Received: 19 March 2012
Accepted: 17 July 2012

Abstract

We show how the equation-free approach can be exploited to enable agent-based simulators to perform system-level computations such as bifurcation, stability analysis and controller design. We illustrate these tasks through an event-driven agent-based model describing the dynamic behaviour of many interacting investors in the presence of mimesis. Using short bursts of appropriately initialized runs of the detailed, agent-based simulator, we construct the coarse-grained bifurcation diagram of the (expected) density of agents and investigate the stability of its multiple solution branches. When the mimetic coupling between agents becomes strong enough, the stable stationary state loses its stability at a coarse turning point bifurcation. We also demonstrate how the framework can be used to design a wash-out dynamic controller that stabilizes open-loop unstable stationary states even under model uncertainty.