Emergence of ultradiscrete states due to phase lock caused by saddle-node bifurcation in discrete limit cycles

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