The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains.

The response characteristics of the BVP (Bonhoeffer-van der Pol or FitzHugh-Nagumo) neuronal model to periodic pulse trains were investigated. The global bifurcation structure of model relative to stimulus intensity and period were analyzed using a one-dimensional mapping called the phase transition curve (PTC) extended by Maginu. The PTC clarified how periodic and chaotic responses bifurcate and revealed in particular several examples of chaotic responses bifurcating through period-doubling bifurcations, as well as the coexistences at the same parameter values, of two different periodic orbits, or of a chaotic and a periodic responses.