Frank Schilder, University of Bristol

<H3>Algorithms for Arnol'd Tongues and Quasiperiodic Tori</H3>

This paper presents algorithms for the computation of Arnol'd 
tongues and quasi-periodic tori 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 tori for user-defined rotation numbers. Since 
Arnol'd tongues are approximated by solutions of two-point boundary value 
problems, their computation becomes immediately accessible to a user of 
standard continuation software like, for example, AUTO.}