Oscillatory response in a sensory network of ON and OFF cells with instantaneous and delayed recurrent connections.

A neural field model with multiple cell-to-cell feedback connections is investigated. Our model incorporates populations of ON and OFF cells, receiving sensory inputs with direct and inverted polarity, respectively. Oscillatory responses to spatially localized stimuli are found to occur via Andronov-Hopf bifurcations of stationary activity. We explore the impact of multiple delayed feedback components as well as additional excitatory and/or inhibitory non-delayed recurrent signals on the instability threshold. Paradoxically, instantaneous excitatory recurrent terms are found to enhance network responsiveness by reducing the oscillatory response threshold, allowing smaller inputs to trigger oscillatory activity. Instantaneous inhibitory components do the opposite. The frequency of these response oscillations is further shaped by the polarity of the non-delayed terms.