  We propose an approach to study small limit cycle bifurcations on a center
manifold in analytic or smooth systems depending on parameters. We then apply
it to the investigation of limit cycle bifurcations in a model of calcium
oscillations in the cilia of olfactory sensory neurons and show that it can
have two limit cycles: a stable cycle appearing after a Bautin (generalized
Hopf) bifurcation and an unstable cycle appearing after a subcritical Hopf
bifurcation.
