Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in
Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in
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 neighbors' opinions. For agents with independent identically distributed (i.i.d.) 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 the agents are split into two factions with opposite preferences. 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 destabilize at a coarse symmetry-breaking bifurcation
equation-free methods, agent based models, multiple-scale analysis
1583-1619
Avitabile, Daniele
048f5fc9-dd44-483f-8e28-343d1f6e0af7
Hoyle, Rebecca
e980d6a8-b750-491b-be13-84d695f8b8a1
Samaey, Giovanni
bf78b0fe-ebaa-4945-af09-cd30a9864285
18 November 2014
Avitabile, Daniele
048f5fc9-dd44-483f-8e28-343d1f6e0af7
Hoyle, Rebecca
e980d6a8-b750-491b-be13-84d695f8b8a1
Samaey, Giovanni
bf78b0fe-ebaa-4945-af09-cd30a9864285
Avitabile, Daniele, 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 Systems, 13 (4), .
(doi:10.1137/140962188).
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 neighbors' opinions. For agents with independent identically distributed (i.i.d.) 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 the agents are split into two factions with opposite preferences. 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 destabilize at a coarse symmetry-breaking bifurcation
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avitabile_hoyle_samaey.pdf
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More information
Accepted/In Press date: 3 September 2014
e-pub ahead of print date: 26 September 2014
Published date: 18 November 2014
Keywords:
equation-free methods, agent based models, multiple-scale analysis
Organisations:
Applied Mathematics
Identifiers
Local EPrints ID: 374372
URI: http://eprints.soton.ac.uk/id/eprint/374372
ISSN: 1536-0040
PURE UUID: 1b601ce2-7cbf-4501-8b72-5609640f80bf
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Date deposited: 16 Feb 2015 10:22
Last modified: 15 Mar 2024 03:36
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Contributors
Author:
Daniele Avitabile
Author:
Giovanni Samaey
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