Poincaré map approach to limit cycles of a simplified ultradiscrete Sel'kov model

Abstract

Dynamical properties of the two limit cycles in a ultradiscrete Sel'kov model are analytically investigated. We construct a Poincaré map for the limit cycles and reveal their stabilities; one is attracting and the other is repelling. Basins for the limit cycles are identified. It is found that the basin of the repelling limit cycle has self-similar structure. We also review the Poincaré map from the viewpoint of integrable system theory.