On some properties of the coupled Fitzhugh-Nagumo equations

We consider the FitzHugh-Nagumo model describing two neurons electrically coupled via ion flow through gap juctions between them. This model is a simple example of a neural network, which has a vast amount of periodic behaviors. It is shown that system of equations describing this model does not pass the Painleve test. Analysis of stability of system's trivial stationary point is carried out. It is shown that this equilibrium point is not always stable. For some parameter regions where solution oscillates bifurcation diagrams are plotted and Lyapunov exponents are calculated. It is shown that analyzed non-stationary solutions are quasiperiodic.