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.

Topics
Nonlinear systems, Piecewise linear model, Numerical methods, Dynamical systems, Phase space methods, Recurrence relations
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