A non-autonomous bursting model for neurons

Certain mammalian visual neurons exhibit On and Off responses when given a light stimulus. In addition to these responses, [51] showed that for retinal ganglion cells, the neuron will also exhibit a Mixed response when given two simultaneous stimuli in different regions of the cell's receptive field. This Mixed response is a nonlinear combination of the On and Off responses. In this dissertation, a single cell model which can reproduce On, Off, and Mixed responses is developed and examined using leading order analyses and averaging. This model is developed from a current balance equation which includes a non-autonomous input I( t), and consists of three coupled, first-order nonlinear differential equations which describe the dynamics of the membrane potential of the cell. When I(t) is assumed to be a constant current pulse, the On and Off responses can be reproduced but will depend on both the duration and the amplitude of the input. When I(t) is assumed to be monotone slowly decreasing, the model can reproduce the nonlinear properties for two simultaneous stimuli. In this dissertation, conditions which will guarantee each type of response will be found using the different subsystems of the model.