Complex/Dynamical Systems Seminar - Zachary Kilpatrick

Wave initiation thresholds in neural fields: An interface dynamics approach

Traveling waves of neural activity have been observed in vitro and in vivo, resulting for instance from sensory inputs at nucleate outward propagating fronts. However, it can be difficult in both experiments and models to identify the threshold stimulus necessary for wave imitation and propagation. Neural field equations are often used to model population dynamics of large-scale networks of neurons. 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 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 explicit conditions for the portion of the neural field that must be activated for traveling fronts to be initiated in a purely excitatory neural field. This is joint work with Gregory Faye from Institut de Mathématiques de Toulouse.