Investigations of the Fitzhugh-Nagumo neuron model
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Neurons are cells in the body that transmit information to the brain and the body by amplifying an incoming stimulus (electrical charge input) and transmitting it to neighboring neurons, then turning off to be ready for the nextstimulus. These cells also have fast and slow mechanisms to open ion channels in response to electrical charges. Voltage‐gated channels exist for each kind of ion, which open and close in response to voltage difference. If the electrical excitation reaches a sufficiently high level, called an action potential, the neuron fires and transmits the excitations to other neurons. In this work we are modeling neuron action by a nonlinear system of differential equations and investigating properties of our model analytically and numerically to demonstrate its behavior. This work will help individuals studying neuroscience, biology, and/or psychology correlate neural behavior with mathematical models.