Abstract: We develop a multiple shooting parameterization method for studying
stable/unstable manifolds attached to periodic orbits of systems whose dynamics is
determined by an implicit rule. We represent the local invariant manifold using high order
polynomials and show that the method leads to efficient numerical calculations.
We implement the method for several example systems in dimension two and three. The
resulting manifolds provide useful information about the orbit structure of the implicit
system even in the case that the implicit relation is neither invertible nor single-valued.
Authors:
Archana Neupane Timsina and J.D. Mireles James
Preprint:
(Submitted).
MatLab codes: