Journal article
Noise-driven bifurcations in a neural field system modelling networks of grid cells
- Abstract:
- The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity generated by networks of grid cells emerge from the instability of homogeneous activity for small levels of noise. This is carried out by upscaling a noisy grid cell model to a system of partial differential equations in order to analyse the robustness of network activity patterns with respect to noise. Inhomogeneous network patterns are numerically understood as branches bifurcating from unstable homogeneous states for small noise levels. We prove that there is a phase transition occurring as the level of noise decreases. Our numerical study also indicates the presence of hysteresis phenomena close to the precise critical noise value.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.6MB, Terms of use)
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- Publisher copy:
- 10.1007/s00285-022-01811-6
Authors
- Publisher:
- Springer
- Journal:
- Journal of Mathematical Biology More from this journal
- Volume:
- 85
- Article number:
- 42
- Publication date:
- 2022-09-27
- Acceptance date:
- 2022-05-03
- DOI:
- EISSN:
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1432-1416
- ISSN:
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0303-6812
- Language:
-
English
- Keywords:
- Pubs id:
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1195596
- Local pid:
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pubs:1195596
- Deposit date:
-
2022-05-14
Terms of use
- Copyright holder:
- Carrillo et al
- Copyright date:
- 2022
- Rights statement:
- © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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