Modeling sequential cognitive states via population level cortical dynamics

TL;DR

This paper introduces a mathematical neural model combining heteroclinic dynamics with neural-field models to simulate sequential brain activity patterns, exemplified through meditation-related cognitive state transitions.

Contribution

It develops a novel approach to approximate heteroclinic cycles in neural dynamics using high-dimensional neural networks, bridging theoretical models and neuronal processes.

Findings

The model reproduces sequential cognitive state transitions during meditation.

Heteroclinic cycles can be approximated by neural networks interpreted as neural-field systems.

The approach provides a neural interpretation of complex dynamic patterns.

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.