Mean field game problem for the optimal control of neuronal spiking activity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909431467343872 |
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| author | Bo, Lijun Yang, Dongfang Wang, Shihua |
| author_facet | Bo, Lijun Yang, Dongfang Wang, Shihua |
| contents | We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to synchronize with others, thereby giving rise to a finite-player game problem. To address this, we first examine the corresponding mean field game problem and characterize the mean field equilibrium by solving a fixed point problem. Subsequently, leveraging the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the finite-player game as the number of neurons is large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean field game problem for the optimal control of neuronal spiking activity Bo, Lijun Yang, Dongfang Wang, Shihua Optimization and Control We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to synchronize with others, thereby giving rise to a finite-player game problem. To address this, we first examine the corresponding mean field game problem and characterize the mean field equilibrium by solving a fixed point problem. Subsequently, leveraging the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the finite-player game as the number of neurons is large. |
| title | Mean field game problem for the optimal control of neuronal spiking activity |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.12682 |