Modeling sequential cognitive states via population level cortical dynamics
M Virginia Bolelli, Luca Greco, Dario Prandi
arXiv Preprint Archive May 4, 2026 preprint
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Case report |
|---|---|
| Keywords | Math.ds Q-bio.nc |
| Key points | Argues that spatial-discrete neural-field equations with biologically realistic equilibria cannot support heteroclinic cycles, but a neural network approximation of heteroclinic dynamics can generate periodic trajectories that reproduce sequential cognitive state transitions, as demonstrated in a focused-attention meditation case study. |
Abstract
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.