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Effects Of Growth On The Synchronization Of Discrete-Time Dynamical Networks

Juan Gonzalo Barajas Ramirez, Andrés Anzo Hernández
Most real-world networks evolve, that is, new nodes and links are attached or removed from the network. In this work we investigate the effects of growth processes on the synchronized behavior of discrete-time dynamical network. In particular, we consider a network composed of identical Logistic Map, we assume that new nodes are attached to the network according to the model proposed by Barabasi and Albert (BA). We propose that nodes are add sufficiently slowly to the network, that is each growth event occurs after sufficient time has passed from the previous, so that the
transitory effects have die out. We numerically investigate the synchronizability of the network as the number of nodes increases from an initial size. The synchronization criterion for dynamical networks with fixed structure is used as an indication of the stability of the resulting networks. Our results show that the synchronized solution remains attractive only for a limited number of additional nodes. Furthermore, the number
of additional such that synchronization is not lost directly depends on the structure and size of the initial network.
CYBERNETICS AND PHYSICS, Vol. 2, No. 4, 199–204.
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