  Max-plus equations are derived from tropically discretized Sel'kov model via
ultradiscretization. These max-plus equations possess common dynamical
structures with the discretized model: Neimark-Sacker bifurcation and limit
cycles. The limit cycles of the ultradiscrete max-plus equations have seven
discrete states. Furthermore, these max-plus equations exhibit excitability.
Relationship between the tropically discretized model and the derived max-plus
equations is also discussed based on numerical results. It is found that the
derived max-plus equations correspond to a limiting case of the tropically
discretized model.
