Threshold of front propagation in neural fields: An interface dynamics approach

TL;DR

This paper develops an interface-based approach to analyze the threshold conditions for wave initiation in neural fields, providing explicit equations and asymptotic estimates for traveling front dynamics in excitatory neural networks.

Contribution

It introduces a novel interface method to determine activation thresholds and wave initiation conditions in neural fields, extending analysis beyond equilibrium states.

Findings

Derived explicit equations for active regions in neural fields.

Provided asymptotic estimates for wave spreading speeds.

Analyzed conditions for wave initiation in excitatory neural networks.

Abstract

Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in the wave coordinate frame. Nonequilibrium dynamics are more challenging to study, due to the nonlinearity and nonlocality of neural fields, whose interactions are described by the kernel of an integral term. Here, we leverage interface methods to describe the threshold of wave initiation away from equilibrium. In particular, we focus on traveling front initiation in an excitatory neural field. In a neural field with a Heaviside firing rate, neural activity can be described by the dynamics of the interfaces, where the neural activity is at the firing threshold. This allows us to derive conditions for the portion of the neural field that must be activated for traveling fronts to be initiated in a purely excitatory neural field. Explicit equations are possible for a single active (superthreshold) region, and special cases of multiple disconnected active regions. The dynamic spreading speed of the excited region can also be approximated asymptotically. We also discuss extensions to the problem of finding the critical spatiotemporal input needed to initiate waves.