  Dynamical properties of a generalized max-plus model for ultradiscrete limit
cycles are investigated.This model includes both the negative feedback model
and the Sel'kov model. It exhibits the Neimark-Sacker bifurcation, and
possesses stable and unstable ultradiscrete limit cycles. The number of
discrete states in the limit cycles can be analytically determined and its
approximate relation is proposed. Additionally, relationship between the
max-plus model and the two-dimensional normal form of the border collision
bifurcation is discussed.
