Example of simplest bifurcation diagram for a monotone family of vector fields on a torus

TL;DR

This paper provides an example of a simple bifurcation diagram for a monotone two-parameter vector field family on a torus, confirming the theoretical class of diagrams proposed by previous researchers.

Contribution

It demonstrates the realizability of the 'simplest' bifurcation diagrams for a specific class of vector fields on a torus.

Findings

The bifurcation diagram belongs to the class proposed by Baesens & MacKay.

The example confirms the theoretical possibility of such simple diagrams.

It advances understanding of bifurcation structures in dynamical systems on tori.

Abstract

We present an example of a monotone two-parameter family of vector fields on a torus whose bifurcation diagram we demonstrate to be in the class of "simplest" diagrams proposed by Baesens & MacKay (2018 Nonlinearity 31 2928--81). This shows that the proposed class is realisable.