Modeling sequential cognitive states via population level cortical dynamics

In a paper submitted to arXiv on May 4, 2026, researchers M. Virginia Bolelli, Luca Greco, and Dario Prandi from L2S and CNRS tackle a fundamental challenge in computational neuroscience: modeling sequential and cyclic patterns of brain activity. They first demonstrate that standard spatial-discrete neural-field equations with biologically realistic equilibria cannot support heteroclinic cycles—the mathematical structures that underpin transitions between distinct cognitive states. However, such dynamics arise naturally in Lotka-Volterra systems, which don't directly map to neuronal processes.

To bridge this gap, the team leverages a version of the Universal Approximation Theorem to build a high-dimensional Amari-type neural-field system that approximates any target dynamics containing a heteroclinic cycle. The resulting vector field generates a periodic trajectory that closely follows the heteroclinic connections. As a concrete case study, they model the cognitive processes underlying focused-attention meditation, showing how the model reproduces sequential transitions among meditative states. This work offers a mathematically rigorous framework for understanding how the brain moves between different cognitive modes, with potential implications for neuroscience and AI.