Fluctuation-response relation unifies dynamical behaviors in neural fields

Anticipation is a strategy used by neural fields to compensate for transmission and processing delays during the tracking of dynamical information and can be achieved by slow, localized, inhibitory feedback mechanisms such as short-term synaptic depression, spike-frequency adaptation, or inhibitory feedback from other layers. Based on the translational symmetry of the mobile network states, we derive generic fluctuation-response relations, providing unified predictions that link their tracking behaviors in the presence of external stimuli to the intrinsic dynamics of the neural fields in their absence.