Generating velocity tuning by asymmetric recurrent connections

Asymmetric lateral connections are one possible mechanism that can ac- count for the direction selectivity of cortical neurons. We present a math- ematical analysis for a class of these models. Contrasting with earlier theoretical work that has relied on methods from linear systems theory, we study the network's nonlinear dynamic properties that arise when the threshold nonlinearity of the neurons is taken into account. We show that such networks have stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. In addition, our analysis shows that outside a certain regime of stimulus speeds the stability of this solutions breaks down giving rise to another class of solutions that are characterized by specific spatio- temporal periodicity.