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Chimera states are complex spatio-temporal patterns that consist ofcoexisting domains of coherent and incoherent dynamics. We analyse chimerastates in networks of Van der Pol oscillators with hierarchical couplingtopology. We investigate the stepwise transition from a nonlocal to ahierarchical topology, and propose the network clustering coefficient as ameasure to establish a link between the existence of chimera states and thecompactness of the initial base pattern of a hierarchical topology; we showthat a large clustering coefficient promotes the occurrence of chimeras.Depending on the level of hierarchy and base pattern, we obtain chimera stateswith different numbers of incoherent domains. We investigate the chimeraregimes as a function of coupling strength and nonlinearity parameter of theindividual oscillators. The analysis of a network with larger base patternresulting in larger clustering coefficient reveals two different types ofchimera states and highlights the increasing role of amplitude dynamics.

Chimera states in hierarchical networks of Van der Pol oscillators