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Non-locally coupled oscillators with a phase lag exhibit various non-trivialspatio-temporal patterns such as the chimera states and the multi-twistedstates. We numerically study large-scale spatio-temporal patterns in a ring ofoscillators with a repulsive coupling with a phase delay parameter $\alpha$. Wefind that the multi-chimera state disappears when $\alpha$ exceeds a criticalvalue. Analyzing the density of incoherent regions, we show that the transitionis analogous to that of directed percolation with two absorbing states, buttheir critical behaviors are different. The multi-chimera state reappears when$\alpha$ is further increased, exhibiting non-trivial spatio-temporal patternswith a plateau in the density of incoherent regions. A transition from themulti-chimera to multi-twisted states follows at a larger value of $\alpha$,resulting in five collective phases in total.

Large-scale spatio-temporal patterns in a ring of non-locally coupled oscillators with a repulsive coupling