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Abstract:
Asymmetric lateral connections are one possible mechanism that
can account for the direction selectivity of cortical neurons. We
present a mathematical 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 cortex is mainly
achieved by asymmetric lateral connections lurching activity
waves might be observable in ensembles of direction selective
cortical neurons within appropriate regimes of the stimulus
speed.
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