A FitzHugh Differential-Difference Equation Modeling Recurrent Neural Feedback
Richard E. Plant
Source abstract
A very simple model based on the FitzHugh equations is developed to simulate the phenomenon of recurrent neural feedback. This phenomenon, which is ubiquitous in the vertebrate nervous system, occurs when a neuron excites a second neuron which in turn excites or inhibits the first neuron. Since the excitation or inhibition occurs only after conduction and synaptic delays, the model involves a system of differential-difference equations. Conditions for the existence of a Hopf bifurcation are derived, and formulas for the stability of the bifurcation are given. Some numerical results for large amplitude solutions are presented. A discussion of the applicability of the model is given.
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