A Numerical Algorithm for Advancing Slow Features in Fast-Slow Systems without Scale Separation, A Y

In the first part of the talk, and in
order to set the stage, we will offer a
multi-scale and averaging strategy to compute the
solution of a singularly perturbed system when the
fast dynamics oscillates rapidly; namely, the fast
dynamics forms cycle-like limits which advance
along with the slow dynamics. We describe the limit
as a Young measure with values being supported on
the limit cycles, averaging with respect to which
induces the equation for the slow dynamics. In
particular, computing the tube of the limit cycles
establishes a good approximation for arbitrarily
small singular parameters. We will demonstrate this
by exhibiting concrete numerical examples.