Modeling sequential cognitive states via population level cortical dynamics
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| Format: | Preprint |
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2026
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| _version_ | 1866917457596252160 |
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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 |
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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 |