  Spiral wave chimeras (SWCs), which combine the features of spiral waves and
chimera states, are a new type of dynamical patterns emerged in spatiotemporal
systems due to the spontaneous symmetry breaking of the system dynamics. In
generating SWC, the conventional wisdom is that the dynamical elements should
be coupled in a nonlocal fashion. For this reason, it is commonly believed that
SWC is excluded from the general reaction-diffusion (RD) systems possessing
only local couplings. Here, by an experimentally feasible model of
three-component FitzHugh-Nagumo-type RD system, we demonstrate that, even
though the system elements are locally coupled, stable SWCs can still be
observed in a wide region in the parameter space. The properties of SWCs are
explored, and the underlying mechanisms are analyzed from the point view of
coupled oscillators. Transitions from SWC to incoherent states are also
investigated, and it is found that SWCs are typically destabilized in two
scenarios, namely core breakup and core expansion. The former is characterized
by a continuous breakup of the single asynchronous core into a number of small
asynchronous cores, whereas the latter is featured by the continuous expansion
of the single asynchronous core to the whole space. Remarkably, in the scenario
of core expansion, the system may develop into an intriguing state in which
regular spiral waves are embedded in a completely disordered background. This
state, which is named shadowed spirals, manifests from a new perspective the
coexistence of incoherent and coherent states in spatiotemporal systems,
generalizing therefore the traditional concept of chimera states. Our studies
provide an affirmative answer to the observation of SWCs in RD systems, and
pave a way to the realization of SWCs in experiments.
