IbexCont1 is a plugin for Ibex (http://www.ibex-lib.org/) implementing the ParCont and BoxCont algorithm from my paper:
Certified Parallelotope Continuation for One-Manifolds, SIAM Journal on Numerical Analysis, Volume 51(6), Pages 3373-3401, 2013
The sources are available on my github page at https://github.com/benjam-art-in/IbexCont. The project is under LGPL.