Sensitivity of neuron oscillators to stimulation frequency

Abstract

This project is motivated by unexplained observations made in experiments with the stomatogastric nervous system of some crustaceans. The oscillatory activity of its neurons seemed to be selectively cancelled by dopamine shots. The idea is to use the theory of Response Functions to give an explanation to this phenomena from a more theoretical point of view. It includes the application of the parameterization method, the computation of the isochrons of the system and the implementation of an interpolative method to obtain the Phase and Amplitude Respose Functions. We will analyse a two dimensional version of the Hodgkin-Huxley model, finding its periodic solution and studying the resulting effects of adding perturbations to the system.