Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator

A neurobiologically motivated relaxation oscillator was used to study the response of an excitable neurons to pulsatile stimulation. The study employed an extended isochronal map, derived from the geometric singular perturbation theory. The presence of an attracting invariant manifold was employed for the construction of the Fenichel normal form for the system. The isochronal maps depicted a single discontinuity and admitted mode-locked, quasiperiodic and chaotic responses.