  We study a system of phase oscillators with nonlocal coupling in a ring that
supports self-organized patterns of coherence and incoherence, called chimera
states. Introducing a global feedback loop, connecting the phase lag to the
order parameter, we can observe chimera states also for systems with a small
number of oscillators. Numerical simulations show a huge variety of regular and
irregular patterns composed of localized phase slipping events of single
oscillators. Using methods of classical finite dimensional chaos and
bifurcation theory, we can identify the emergence of chaotic chimera states as
a result of transitions to chaos via period doubling cascades, torus breakup,
and intermittency. We can explain the observed phenomena by a mechanism of
self-modulated excitability in a discrete excitable medium.
