Exact solution of the nonlinear dynamics of recurrent neural mechanisms for direction selectivity

摘要

Different theoretical models have tried to investigate the feasibility of recurrent neural mecha- nisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the re- sponses of direction selective cortical neurons.