Linear control systems on a 4D solvable Lie group used to model primary visual cortex V1

2025/10/31 by Adriano Da Silva, Da Silva, Adriano, Eyüp Kızıl +3
Neuroscience · Computer Science · Medicine · #Visual perception and processing mechanisms #Advanced Vision and Imaging #Glaucoma and retinal disorders

paper · pdf · doi:10.48550/arxiv.2510.27445

Abstract

In this article, we study linear control systems on a 4-dimensional solvable Lie group. Our motivation stems from the model introduced in \citebaspinar, 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 ℝ²), with orientation θ∈ S¹, spatial frequency ω∈ ℝ⁺, and phase ϕ∈ S¹ as intrinsic parameters. For each fixed frequency ω, this model defines a Lie group G(ω) = ℝ² × S¹ × S¹, 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.

Citations

• One-input linear control systems on the homogeneous spaces of the Heisenberg group -- The singular case
• Equivalence of Control Systems with Linear Systems on Lie Groups and Homogeneous Spaces

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