Abstract
We study fully synchronized states in scale-free networks of chaotic
logistic maps as a function of both dynamical and topological
parameters. Three different network topologies are considered: (i) a
random scale-free topology, (ii) a deterministic pseudofractal
scale-free network, and (iii) an Apollonian network. For the random
scale-free topology we find a coupling strength threshold beyond which
full synchronization is attained. This threshold scales as k(-mu), where
k is the outgoing connectivity and mu depends on the local nonlinearity.
For deterministic scale-free networks coherence is observed only when
the coupling strength is proportional to the neighbor connectivity. We
show that the transition to coherence is of first order and study the
role of the most connected nodes in the collective dynamics of
oscillators in scale-free networks.
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