Dynamical properties of max-plus equations obtained from tropically discretized Sel'kov model

TL;DR

This paper derives max-plus equations from a tropically discretized Sel'kov model, revealing their dynamical behaviors such as bifurcations, limit cycles, and excitability, and explores their relationship with the original discretized model.

Contribution

It introduces a novel derivation of max-plus equations from the discretized Sel'kov model and analyzes their dynamical properties and relationship to the original system.

Findings

Max-plus equations exhibit Neimark-Sacker bifurcation and limit cycles.

Limit cycles have seven discrete states.

Max-plus equations show excitability.

Abstract

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.