SYNCHRONIZATION ON GROWING DYNAMICAL
NETWORKS: A DISCRETE EVENT APPROACH
We investigate dynamical networks with structural
evolution, i.e. nodes and edges are added or deleted as
the network adapts to the realities of its environment.
We focus on dynamical networks with a given initial
structure where the evolution consists exclusively of
growth events, further we assume that the growth process
that shapes the network structure follows the wellknown
Barabási-Albert (BA) model. In particular, we
analyze the effects of the growth process on the stability
of the collective dynamical behavior of the network.
To this end, we model the growth process as a
discrete-event process on the dynamical network. Our
results show that the stability of the synchronized solution
is preserved for the addition of only a limited
number of nodes. Furthermore, the number of added
nodes for which the stability is preserved directly depends
on the structure and size of the initial structure
of the network.