  The recently discovered chimera state involves the coexistence of
synchronized and desynchronized states for a group of identical oscillators.
This fascinating chimera state has until now been found only in non-local or
globally coupled oscillator systems. In this work, we for the first time show
numerical evidence of the existence of spiral wave chimeras in
reaction-diffusion systems where each element is locally coupled by diffusion.
This spiral wave chimera rotates inwardly, i.e., coherent waves propagate
toward the phase randomized core. A continuous transition from spiral waves
with smooth core to spiral wave chimeras is found as we change the local
dynamics of the system. Our findings on the spiral wave chimera in locally
coupled oscillator systems largely improve our understanding of the chimera
state and suggest that spiral chimera states may be found in natural systems
which can be modeled by a set of oscillators indirectly coupled by a diffusive
environment.
