  The Pyragas method of feedback control has attracted much interest as a
method of stabilising unstable periodic orbits in a number of situations. We
show that a time-delayed feedback control similar to the Pyragas method can be
used to stabilise periodic orbits with arbitrarily large period, specifically
those resulting from a resonant bifurcation of a heteroclinic cycle. Our
analysis reduces the infinite-dimensional delay-equation governing the system
with feedback to a three-dimensional map, by making certain assumptions about
the form of the solutions. The stability of a fixed point in this map
corresponds to the stability of the periodic orbit in the flow, and can be
computed analytically. We compare the analytic results to a numerical example
and find very good agreement.
