  Dynamical properties of limit cycles in a tropically discretized negative
feedback model are numerically investigated. This model has a controlling
parameter $\tau$, which corresponds to time interval for the time evolution of
phase in the limit cycles. By considering $\tau$ as a bifurcation parameter, we
find that ultradiscrete state emerges due to phase lock caused by saddle-node
bifurcation. Furthermore, focusing on limit cycles for the max-plus negative
feedback model, it is found that the unstable limit cycle in the max-plus model
corresponds to the unstable fixed points emerging by the saddle-node
bifurcation in the tropically discretized model.
