{"ID":2847603,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27445","arxiv_id":"2510.27445","title":"Linear control systems on a 4D solvable Lie group used to model primary visual cortex $V1$","abstract":"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.","short_abstract":"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 $\\m...","url_abs":"https://arxiv.org/abs/2510.27445","url_pdf":"https://arxiv.org/pdf/2510.27445v1","authors":"[\"Adriano Da Silva\",\"Eyüp Kizil\",\"Victor Ayala\"]","published":"2025-10-31T12:53:28Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}