Modeling sequential cognitive states via population level cortical dynamics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917457596252160 |
|---|---|
| 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 |