Xiaohui Xie, Martin Giese
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. This predicts that if direction selectivity in the cor- tex is mainly achieved by asymmetric lateral connections lurching activ- ity waves might be observable in ensembles of direction selective cortical neurons within appropriate regimes of the stimulus speed.