Alan Lloyd Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology for their work describing the propogation of action potentials in the squid giant axon. Major analysis of their system of differential equations was performed by Richard FitzHugh, and later on by Jin-ichi Nagumo who created a tunnel diode circuit based upon FitzHugh's work. The subsequent differential equation model, known as the FitzHugh-Nagumo (FH-N) oscillator, represents a simplification of the Hodgkin-Huxley (H-H) model, but still replicates the original neuronal dynamics. This thesis begins by providing a thorough grounding in the physiology behind the equations. We continue by proving some of the results postulated by Tanya Kostova et al. for FH-N without forcing. Finally, this sets up our own exploration into stimulating the system with smooth periodic forcing. Subsequent quantification of the chaotic phase portraits using a Lyapunov exponent are discussed, as well as the relevance of these results to electrocardiography.
"Stability Analysis of FitzHugh–Nagumo with Smooth Periodic Forcing,"
Proceedings of GREAT Day: Vol. 2011, Article 4.
Available at: https://knightscholar.geneseo.edu/proceedings-of-great-day/vol2011/iss1/4