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We study chimera states, which are partial synchronization patternsconsisting of spatially coexisting domains of coherent (synchronized) andincoherent (desynchronized) dynamics, in ring networks of FitzHugh-Nagumooscillators with fractal connectivities. In particular, we focus on theinterplay of time delay in the coupling term and the network topology. In theparameter plane of coupling strength and delay time we find tongue-like regionsof existence of chimera states alternating with regions of coherent dynamics.We show analytically and numerically that the period of the synchronizeddynamics as a function of delay is characterized by a sequence of piecewiselinear branches. In between these branches various chimera states and otherpartial synchronization patterns are induced by the time delay. By varying thetime delay one can deliberately choose and stabilize desired spatio-temporalpatterns.

Delay-induced chimeras in neural networks with fractal topology