Example of simplest bifurcation diagram for a monotone family of vector fields on a torus**M H-D. was supported by ‘la Caixa’ Foundation (ID 100010434) with fellowship code LCF/BQ/EU20/11810061, and by the Warwick Mathematics Institute Centre for Doctoral Training with funding from the University of Warwick.

Abstract

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 and MacKay (2018 Nonlinearity 31 2928–81). This shows that the proposed class is realisable.