Chimera-Like Coexistence of Synchronized Oscillation and Death in an Ecological Network

We report a novel spatiotemporal state, namely the chimera-like incongruous coexistence of {\it synchronized oscillation} and {\it stable steady state} (CSOD) in a realistic ecological network of nonlocally coupled oscillators. Unlike the {\it chimera} and {\it chimera death} state, in the CSOD state identical oscillators are self-organized into two coexisting spatially separated domains: In one domain neighboring oscillators show synchronized oscillation and in another domain the neighboring oscillators randomly populate either a synchronized oscillating state or a stable steady state (we call it a death state). We show that the interplay of nonlocality and coupling strength results in two routes to the CSOD state: One is from a coexisting mixed state of amplitude chimera and death, and another one is from a globally synchronized state. We further explore the importance of this study in ecology that gives a new insight into the relationship between spatial synchrony and global extinction of species.