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1	Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity Giese, M.A., Xie, X. 01 August 2002 (has links) Different theoretical models have tried 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. 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 responses of direction selective cortical neurons. Our analysis shows also 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. AI direction visual cortex nonlinear dynamics lurching waves stability recurre
2	DISCRETE ANALYSIS OF SYNCHRONIZED OSCILLATIONS IN EXCITATORY-INHIBITORY NEURONAL NETWORKS Zeki, Mustafa 25 October 2010 (has links) No description available. Bioinformatics Mathematics Neurology oscillatory synchronized reduction discrete analysis neuronal networks neron olfactory system working memory lurching waves wave speed transiently synchronized

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

DISCRETE ANALYSIS OF SYNCHRONIZED OSCILLATIONS IN EXCITATORY-INHIBITORY NEURONAL NETWORKS