Algorithms for Arnol'd tongues and quasi-periodic tori : a case study

This paper presents algorithms for the computation of Arnol'd tongues and quasi-periodic curves in a two-parameter plane and demonstrates their performance with an example from nonlinear electrical engineering. Both methods are complementary and, together, allow the computation of the two-parameter bifurcation diagram near a one-parameter family of tori with parallel flow. The algorithms are simple to implement and compute Arnol'd tongues or quasi-periodic curves for user-defined rotation numbers.