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We study a network of coupled logistic maps whose interactions occur with acertain distribution of delay times. The local dynamics is chaotic in theabsence of coupling and thus the network is a paradigm of a complex system.There are two regimes of synchronization, depending on the distribution ofdelays: when the delays are sufficiently heterogeneous the network synchronizeson a steady-state (that is unstable for the uncoupled maps); when the delaysare homogeneous, it synchronizes in a time-dependent state (that is eitherperiodic or chaotic). Using two global indicators we quantify thesynchronizability on the two regimes, focusing on the roles of the networkconnectivity and the topology. The connectivity is measured in terms of theaverage number of links per node, and we consider various topologies(scale-free, small-world, star, and nearest-neighbor with and without a centralhub). With weak connectivity and weak coupling strength, the network displaysan irregular oscillatory dynamics that is largely independent of the topologyand of the delay distribution. With heterogeneous delays, we find a thresholdconnectivity level below which the network does not synchronize, regardless ofthe network size. This minimum average number of neighbors seems to beindependent of the delay distribution. We also analyze the effect ofself-feedback loops and find that they have an impact on the synchronizabilityof small networks with large coupling strengths. The influence of feedback,enhancing or degrading synchronization, depends on the topology and on thedistribution of delays.

Synchronizability of chaotic logistic maps in delayed complex networks