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Nonlinear wave formation and propagation on a complex network with excitablenode dynamics is of fundamental interest in diverse fields in science andengineering. Here, we propose a new model of the Kuramoto type to studynonlinear wave generation and propagation on circular subgraphs of a complexnetwork. On circle networks, in the continuum limit, this model is equivalentto the over-damped Frenkel-Kontorova model. The new model is shown to keep theessential features of those well-known models such as the diffusively coupledB\"ar-Eiswirth model but with much simplified expression such that analyticanalysis becomes possible. We classify traveling wave solutions on circlenetworks and show the universality of its features with perturbation analysisand numerical computation.

Nonlinear waves on circle networks with excitable nodes