Stability and Bifurcation Analysis of Coupled Fitzhugh-Nagumo Oscillators

Understand

Neurons are the central biological objects in understanding how the brain works.

• The famous Hodgkin-Huxley model, which describes how action potentials of a neuron are initiated and propagated, consists of four coupled nonlinear differential equations.
• Because these equations are difficult to deal with, there also exist several simplified models, of which many exhibit polynomial-like non-linearity.
• Examples of such models are the Fitzhugh-Nagumo (FHN) model, the Hindmarsh-Rose (HR) model, the Morris-Lecar (ML) model and the Izhikevich model.