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Wave initiation thresholds in neural fields: AnÌýinterface 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.ÌýNonequilibrium dynamics are moreÌýchallenging to study, due to theÌýnonlinearity and nonlocality of neural fields, whose interactions are described by the kernel ofÌýanÌýintegral term. Here, we leverage interface methods to describe the threshold of wave initiation awayÌýfrom equilibrium. In a neural field with a Heaviside firing rate, neuralÌýactivity can be described by the dynamics of the interfaces, where the neural activity is at the firing threshold. This allows usÌýto derive explicit conditions forÌýthe portion of the neural field that must be activated for traveling fronts to be initiated in a purelyÌýexcitatory neural field. This is joint work with Gregory Faye from Institut de Mathématiques de Toulouse.