On the dynamical behaviour of FitzHugh-Nagumo systems: Revisited

摘要

The purpose of this paper is to analyse a general form of the FitzHugh-Nagumo modelas completely as possible. The main result is that no more than two limit cycles can bebifurcated from the unique fixed point via Hopf bifurcation, and there exist parameterssuch that this upper bound is attained. For these parameters, the stability of the innerand outer cycle, together with the unique fixed point is also established. The resultsare approached through Lyapunov coefficients and rely on a theorem by Andronov andAleksandrovic [A.A. Andronov, A.A. Aleksandrovic, Theory of Bifurcations of DynamicalSystem on a Plane, Wiley, 1971]. Based on singular perturbation theory a sufficientcondition for existence of a unique stable limit cycle is given under certain assumptions.