  Recent evidences show that heteroclinic bifurcations in magnetic islands may
be caused by the amplitude variation of resonant magnetic perturbations in
tokamaks. To investigate the onset of these bifurcations, we consider a large
aspect ratio tokamak with an ergodic limiter composed of two pairs of rings
that create external primary perturbations with two sets of wave numbers. An
individual pair produces hyperbolic and elliptic periodic points, and its
associated islands, that are consistent with the Poincar\'e-Birkhoff fixed
point theorem. However, for two pairs producing external perturbations resonant
on the same rational surface, we show that different configurations of
isochronous island chains may appear on phase space according to the amplitude
of the electric currents in each pair of the ergodic limiter. When one of the
electric currents increases, isochronous bifurcations take place and new
islands are created with the same winding number as the preceding islands. We
present examples of bifurcation sequences displaying (a) direct transitions
from the island chain configuration generated by one of the pairs to the
configuration produced by the other pair, and (b) transitions with intermediate
configurations produced by the limiter pairs coupling. Furthermore, we identify
shearless bifurcations inside some isochronous islands, originating
nonmonotonic local winding number profiles with associated shearless invariant
curves.
