  We study the existence of chimera states in pulse-coupled networks of
bursting Hindmarsh-Rose neurons with nonlocal, global and local (nearest
neighbor) couplings. Through a linear stability analysis, we discuss the
behavior of stability function in the incoherent (i.e. disorder), coherent,
chimera and multi-chimera states. Surprisingly, we find that chimera and
multi-chimera states occur even using local nearest neighbor interaction in a
network of identical bursting neurons alone. This is in contrast with the
existence of chimera states in populations of nonlocally or globally coupled
oscillators. A chemical synaptic coupling function is used which plays a key
role in the emergence of chimera states in bursting neurons. Existence of
chimera, multi-chimera, coherent and disordered states are confirmed by means
of the recently introduced statistical measures and mean phase velocity.
