19 research outputs found
Synchronizabilities of Networks: A New index
The random matrix theory is used to bridge the network structures and the
dynamical processes defined on them. We propose a possible dynamical mechanism
for the enhancement effect of network structures on synchronization processes,
based upon which a dynamic-based index of the synchronizability is introduced
in the present paper.Comment: 4pages, 2figure
Scaling Invariance in Spectra of Complex Networks: A Diffusion Factorial Moment Approach
A new method called diffusion factorial moment (DFM) is used to obtain
scaling features embedded in spectra of complex networks. For an Erdos-Renyi
network with connecting probability , the scaling
parameter is , while for the scaling
parameter deviates from it significantly. For WS small-world networks, in the
special region , typical scale invariance is found. For GRN
networks, in the range of , we have .
And the value of oscillates around abruptly. In the range
of , we have basically . Scale invariance is one
of the common features of the three kinds of networks, which can be employed as
a global measurement of complex networks in a unified way.Comment: 6 pages, 8 figures. to appear in Physical Review
Collective Chaos Induced by Structures of Complex Networks
Mapping a complex network of coupled identical oscillators to a quantum
system, the nearest neighbor level spacing (NNLS) distribution is used to
identify collective chaos in the corresponding classical dynamics on the
complex network. The classical dynamics on an Erdos-Renyi network with the
wiring probability is in the state of collective
order, while that on an Erdos-Renyi network with in the
state of collective chaos. The dynamics on a WS Small-world complex network
evolves from collective order to collective chaos rapidly in the region of the
rewiring probability , and then keeps chaotic up to . The dynamics on a Growing Random Network (GRN) is in a special state
deviates from order significantly in a way opposite to that on WS small-world
networks. Each network can be measured by a couple values of two parameters
.Comment: 15 pages, 12 figures, To appear in Physica