  Chimera states, which consist of coexisting domains of spatially coherent and
incoherent dynamics, have been widely found in nonlocally coupled oscillatory
systems. We demonstrate for the first time that chimera states can emerge from
excitable systems under nonlocal coupling in which isolated units only allow
for the equilibrium. We theoretically reveal that nonlocal coupling induced
collective oscillation is behind the occurrence of the chimera states. We find
two different types of chimera states, phase-chimera state and
excitability-chimera states, depending on the coupling strength. At weak
coupling strength where collective oscillation is localized around the unstable
homogeneous equilibrium, the chimera states are similar to the ones in
nonlocally coupled phase oscillators. For the chimera states at strong coupling
strength, the dynamics of both coherent units and incoherent units shift back
and forth between low amplitude oscillation induced by collective oscillation
and high amplitude oscillation induced by excitability of local units.
