Linear control systems on a 4D solvable Lie group used to model primary visual cortex $V1$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915588599709696 |
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| author | Da Silva, Adriano Kizil, Eyüp Ayala, Victor |
| author_facet | Da Silva, Adriano Kizil, Eyüp Ayala, Victor |
| contents | In this article, we study linear control systems on a 4-dimensional solvable Lie group. Our motivation stems from the model introduced in \cite{baspinar}, which presents a precise geometric framework in which the primary visual cortex $V1$ is interpreted as a fiber bundle over the retinal plane $M$ (identified with $\mathbb{R}^{2}$), with orientation $θ\in S^{1}$, spatial frequency $ω\in \mathbb{R}^{+}$, and phase $ϕ\in S^{1}$ as intrinsic parameters. For each fixed frequency $ω$, this model defines a Lie group $G(ω) = \mathbb{R}^{2} \times S^{1} \times S^{1}$, which we adopt in this work as the state space group $G$ of our linear control system. We also present new results concerning controllability and characterize the control sets associated with this class of systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear control systems on a 4D solvable Lie group used to model primary visual cortex $V1$ Da Silva, Adriano Kizil, Eyüp Ayala, Victor Optimization and Control In this article, we study linear control systems on a 4-dimensional solvable Lie group. Our motivation stems from the model introduced in \cite{baspinar}, which presents a precise geometric framework in which the primary visual cortex $V1$ is interpreted as a fiber bundle over the retinal plane $M$ (identified with $\mathbb{R}^{2}$), with orientation $θ\in S^{1}$, spatial frequency $ω\in \mathbb{R}^{+}$, and phase $ϕ\in S^{1}$ as intrinsic parameters. For each fixed frequency $ω$, this model defines a Lie group $G(ω) = \mathbb{R}^{2} \times S^{1} \times S^{1}$, which we adopt in this work as the state space group $G$ of our linear control system. We also present new results concerning controllability and characterize the control sets associated with this class of systems. |
| title | Linear control systems on a 4D solvable Lie group used to model primary visual cortex $V1$ |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.27445 |