Speed hysteresis and noise shaping of traveling fronts in neural fields: role of local circuitry and nonlocal connectivity.

Neural field models are powerful tools to investigate the richness of spatiotemporal activity patterns like waves and bumps, emerging from the cerebral cortex. Understanding how spontaneous and evoked activity is related to the structure of underlying networks is of central interest to unfold how information is processed by these systems. Here we focus on the interplay between local properties like input-output gain function and recurrent synaptic self-excitation of cortical modules, and nonlocal intermodular synaptic couplings yielding to define a multiscale neural field. In this framework, we work out analytic expressions for the wave speed and the stochastic diffusion of propagating fronts uncovering the existence of an optimal balance between local and nonlocal connectivity which minimizes the fluctuations of the activation front propagation. Incorporating an activity-dependent adaptation of local excitability further highlights the independent role that local and nonlocal connectivity play in modulating the speed of propagation of the activation and silencing wavefronts, respectively. Inhomogeneities in space of local excitability give raise to a novel hysteresis phenomenon such that the speed of waves traveling in opposite directions display different velocities in the same location. Taken together these results provide insights on the multiscale organization of brain slow-waves measured during deep sleep and anesthesia.