2025/04/23 by Hiroshi Ishii, Ishii, Hiroshi, R Watanabe +2 · 1 voice
Biochemistry, Genetics and Molecular Biology · Engineering · Medicine · Physics and Astronomy · #Complex Systems and Dynamics #Elasticity and Wave Propagation #FOS: Biological sciences #FOS: Physical sciences #Neurons and Cognition (q-bio.NC) #Pattern Formation and Solitons (nlin.PS) #Technology and Human Factors in Education and Health #nlin.PS #q-bio.NC
paper · pdf · doi:10.48550/arxiv.2504.16342
openalex publication_date 2025/04/23 · arxiv published 2025/04/23 · openalex created_date 2025/10/11 · arxiv updated 2026/01/20 · openalex updated_date 2026/07/28
Understanding the dynamics of excitation patterns in neural fields is an important topic in neuroscience. Neural field equations are mathematical models that describe the excitation dynamics of interacting neurons to perform the theoretical analysis. Although many analyses of neural field equations focus on the effect of neuronal interactions on the flat surface, the geometric constraint of the dynamics is also an attractive topic when modeling organs such as the brain. This paper reports pattern dynamics in a neural field equation defined on spheroids as model curved surfaces. We treat spot solutions as localized patterns and discuss how the geometric properties of the curved surface change their properties. To analyze spot patterns on spheroids with small flattening, we first construct exact stationary spot solutions on the spherical surface and reveal their stability. We then extend the analysis to show the existence and stability of stationary spot solutions in the spheroidal case. One of our theoretical results is the derivation of a stability criterion for stationary spot solutions localized at poles on oblate spheroids. The criterion determines whether a spot solution remains at a pole or moves away. Finally, we conduct numerical simulations to discuss the dynamics of spot solutions with the insight of our theoretical predictions. Our results show that the dynamics of spot solutions depend on the curved surface and the coordination of neural interactions.