Dynamics of a neuron model with complex-threshold excitation

Dynamical modes of a neuron model with complex-threshold excitation are investigated. The model represents a modification of the classical FitzHugh-Nagumo equations modeling the dynamics of nerve cells. The excitation threshold is described by the separatrix of a saddle fixed point. Depending on system parameters it can have quite complex dynamics. Dynamical mechanisms underlying oscillatory modes and various effects of complex model response on an external perturbation are investigated. In particular, it is found that incoming external stimulus may yield the appearance of response pulse series with different duration as well as single pulse response. Using analytical methods the analysis of local and nonlocal bifurcations has been carried out. Parameters regions corresponding to different dynamical behaviors of the model have been obtained. Bifurcation curves separating different regions are analyzed.