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Chimera states are a phenomenon in which order and disorder can co-existwithin a network that is fully homogeneous. Precisely how transient chimerasemerge in finite networks of Kuramoto oscillators with phase-lag remainsunclear. Utilizing an operator-based framework to study nonlinear oscillatornetworks at finite scale, we reveal the spatiotemporal impact of the adjacencymatrix eigenvectors on the Sakaguchi-Kuramoto dynamics. We identify a specificcondition for the emergence of transient chimeras in these finite networks: theeigenvectors of the network adjacency matrix create a combination of a zerophase-offset mode and low spatial frequency waves traveling in oppositedirections. This combination of eigenvectors leads directly to the coherent andincoherent clusters in the chimera. This approach provides two specificanalytical predictions: (1) a precise formula predicting the combination ofconnectivity and phase-lag that creates transient chimeras, (2) a mathematicalprocedure for rewiring arbitrary networks to produce transient chimeras.

Theory of transient chimeras in finite Sakaguchi-Kuramoto networks