Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911117756858368 |
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| author | Avitabile, Daniele MacLaurin, James |
| author_facet | Avitabile, Daniele MacLaurin, James |
| contents | We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as control parameter the diffusivity strength of the afferent white noise on each neuron. We find conditions for Turing-like bifurcations in a system where the cortex is modelled as a ring, and we produce numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. We provide numerical evidence that solutions of the finite-size network converge weakly to solutions of the mean-field model. Finally, we prove a Large Deviation Principle, which provides a means of assessing the likelihood of deviations from the mean-field equations induced by finite-size effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks Avitabile, Daniele MacLaurin, James Probability Dynamical Systems Neurons and Cognition We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as control parameter the diffusivity strength of the afferent white noise on each neuron. We find conditions for Turing-like bifurcations in a system where the cortex is modelled as a ring, and we produce numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. We provide numerical evidence that solutions of the finite-size network converge weakly to solutions of the mean-field model. Finally, we prove a Large Deviation Principle, which provides a means of assessing the likelihood of deviations from the mean-field equations induced by finite-size effects. |
| title | Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks |
| topic | Probability Dynamical Systems Neurons and Cognition |
| url | https://arxiv.org/abs/2408.12540 |