We study a triangular network of three populations of coupled phase
oscillators with identical frequencies. The populations interact nonlocally, in
the sense that all oscillators are coupled to one another, but more weakly to
those in neighboring populations than to those in their own population. This
triangular network is the simplest discretization of a continuous ring of
oscillators. Yet it displays an unexpectedly different behavior: in contrast to
the lone stable chimera observed in continuous rings of oscillators, we find
that this system exhibits \emph{two coexisting stable chimeras}. Both chimeras
are, as usual, born through a saddle node bifurcation. As the coupling becomes
increasingly local in nature they lose stability through a Hopf bifurcation,
giving rise to breathing chimeras, which in turn get destroyed through a
homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal
of this scenario as we further increase the locality of the coupling, until it
is annihilated through another saddle node bifurcation.Comment: 12 pages, 5 figure
