  Dynamical properties of ultradiscrete Hopf bifurcation, similar to those of
the standard Hopf bifurcation, are discussed by proposing a simple model of
ultradiscrete equations with max-plus algebra. In ultradiscrete Hopf
bifurcation, limit cycles emerge depending on the value of a bifurcation
parameter in the model. The limit cycles are composed of a finite number of
discrete states. Furthermore, the model exhibits excitability. The model is
derived from two different dynamical models with Hopf bifurcation by means of
ultradiscretization; it is a candidate for a normal form for ultradiscrete Hopf
bifurcation.
