Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity

摘要

Different theoretical models have been used to investigate the feasibility of recurrent neural mechanisms 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. In this paper, the authors present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. The mathematical analysis shows that such networks have form- stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. The analysis also shows that the stability of such solutions can break down, giving raise to a different class of solutions ('lurching activity waves') that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering.