Tor: a toolbox for the continuation of two-dimensional tori in autonomous systems and non-autonomous systems with periodic forcing

Abstract

We present a toolbox for the continuation of two-dimensional tori in autonomous dynamical systems and non-autonomous systems with periodic forcing. A torus is solved as the solution to a boundary-value problem. Truncated Fourier series and collocation methods are used to discretize the boundary-value problem. This toolbox is based on the continuation package COCO (https://sourceforge.net/projects/cocotools/). A few examples are included to demonstrate the functionality of this toolbox.