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 neighbours' opinions. For agents with independent...
| Main Authors: | , , |
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| Format: | Article |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | https://eprints.nottingham.ac.uk/3330/ |
| _version_ | 1848791002571079680 |
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| author | Avitabile, Daniele Hoyle, Rebecca Samaey, Giovanni |
| author_facet | Avitabile, Daniele Hoyle, Rebecca Samaey, Giovanni |
| author_sort | Avitabile, Daniele |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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 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. |
| first_indexed | 2025-11-14T18:21:35Z |
| format | Article |
| id | nottingham-3330 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:21:35Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-33302020-05-04T20:16:07Z https://eprints.nottingham.ac.uk/3330/ Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in Avitabile, Daniele Hoyle, Rebecca Samaey, Giovanni 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 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. Society for Industrial and Applied Mathematics 2014 Article NonPeerReviewed 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 System . ISSN 1536-0040 (In Press) http://www.siam.org/journals/siads.php |
| spellingShingle | Avitabile, Daniele Hoyle, Rebecca Samaey, Giovanni Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| title | Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| title_full | Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| title_fullStr | Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| title_full_unstemmed | Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| title_short | Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| title_sort | noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in |
| url | https://eprints.nottingham.ac.uk/3330/ https://eprints.nottingham.ac.uk/3330/ |