The Field–Noyes model with periodic orbits

Abstract

This paper considers the Field–Noyes model. There are two possibilities if we consider only the case that the positive equilibrium of the system p is hyperbolic. Either p is asymptotically stable or it is unstable with a one-dimensional stable manifold. Both cases can occur, depending on the values of the parameters. Condition for the existence of a nontrivial periodic orbit are given in the second case.