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This work explores four nonlinear classical models of neural oscillators, theHodgkin-Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, andthe Hindmarsh-Rose model. Nonlinear contraction theory is used to developobservers and perform synchronization analysis on these systems. Neuraloscillation and signaling models are based on the biological function of theneuron, with behavior mediated through the channeling of ions across the cellmembrane. The variable assumed to be measured is the membrane potential, whichmay be obtained empirically through the use of a neuronal force-clamp system,or may be transmitted through the axon to other neurons. All other variablesare estimated by using partial state or full state observers. Basic observerrate convergence analysis is performed for the Fitzhugh Nagumo system, partialstate observer design is performed for the Morris-Lecar system, and basicsynchronization analysis is performed for both the Fitzhugh-Nagumo and theHodgkin-Huxley systems.

Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators