Modeling sequential cognitive states via population level cortical dynamics

Fuente: arXiv
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Main Authors: Bolelli, M Virginia, Greco, Luca, Prandi, Dario
Format: Preprint
Published: 2026
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author Bolelli, M Virginia
Greco, Luca
Prandi, Dario
author_facet Bolelli, M Virginia
Greco, Luca
Prandi, Dario
contents In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with biologically realistic equilibria cannot support heteroclinic cycles. On the other hand, heterocline dynamics often arise in Lotka-Volterra-type systems, but these equations do not directly correspond to neuronal processes. To address this, we use a version of the Universal Approximation Theorem to approximate any target dynamics by a neural network interpretable as a high-dimensional Amari-type neural-field system. When the target dynamics contains a heteroclinic cycle, the approximating vector field generates a periodic trajectory that closely follows the heteroclinic connection. As a case study, we consider the cognitive processes underlying focused-attention meditation. We show how the model reproduces sequential transitions among cognitive states and we conclude providing a neural interpretation of the approximating dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2605_02365
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Modeling sequential cognitive states via population level cortical dynamics
Bolelli, M Virginia
Greco, Luca
Prandi, Dario
Dynamical Systems
Neurons and Cognition
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with biologically realistic equilibria cannot support heteroclinic cycles. On the other hand, heterocline dynamics often arise in Lotka-Volterra-type systems, but these equations do not directly correspond to neuronal processes. To address this, we use a version of the Universal Approximation Theorem to approximate any target dynamics by a neural network interpretable as a high-dimensional Amari-type neural-field system. When the target dynamics contains a heteroclinic cycle, the approximating vector field generates a periodic trajectory that closely follows the heteroclinic connection. As a case study, we consider the cognitive processes underlying focused-attention meditation. We show how the model reproduces sequential transitions among cognitive states and we conclude providing a neural interpretation of the approximating dynamics.
title Modeling sequential cognitive states via population level cortical dynamics
topic Dynamical Systems
Neurons and Cognition
url https://arxiv.org/abs/2605.02365