Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in

Avitabile, Daniele and Hoyle, Rebecca and Samaey, Giovanni (2014) Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in. SIAM Journal on Applied Dynamical System . ISSN 1536-0040 (Submitted)

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Abstract

We investigate coarse equilibrium states of a fine-scale, stochastic agent-based model of consumer lock-in in a duopolistic market. In the model, agents decide on their next purchase based on a combination of their personal preference and their neighbours' opinions. For agents with independent identically-distributed parameters and all-to-all coupling, we derive an analytic approximate coarse evolution-map for the expected average purchase. We then study the emergence of coarse fronts when spatial segregation is present in the relative perceived quality of products. We develop a novel Newton-Krylov method that is able to compute accurately and efficiently coarse fixed points when the underlying fine-scale dynamics is stochastic. The main novelty of the algorithm is in the elimination of the noise that is generated when estimating Jacobian-vector products using time-integration of perturbed initial conditions. We present numerical results that demonstrate the convergence properties of the numerical method, and use the method to show that macroscopic fronts in this model destabilise at a coarse symmetry-breaking bifurcation.

Item Type: Article
Additional Information: Copyright: Society for Industrial and Applied Mathematics
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Avitabile, Dr. Daniele
Date Deposited: 23 Jul 2014 15:30
Last Modified: 14 Sep 2016 09:04
URI: http://eprints.nottingham.ac.uk/id/eprint/3246

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