In a recent work [Shao $et$ $al$ 2009 Phys. Rev. Lett. textbf{108} 018701], a nonconsensus opinion (NCO) model was proposed, where two opinions can stably coexist by forming clusters of agents holding the same opinion. The NCO model on lattices and s
everal complex networks displays a phase transition behavior, which is characterized by a large spanning cluster of nodes holding the same opinion appears when the initial fraction of nodes holding this opinion is above a certain critical value. In the NCO model, each agent will convert to its opposite opinion if there are more than half of agents holding the opposite opinion in its neighborhood. In this paper, we generalize the NCO model by assuming that each agent will change its opinion if the fraction of agents holding the opposite opinion in its neighborhood exceeds a threshold $T$ ($Tgeq 0.5$). We call this generalized model as the NCOT model. We apply the NCOT model on different network structures and study the formation of opinion clusters. We find that the NCOT model on lattices displays a continuous phase transition. For random graphs and scale-free networks, the NCOT model shows a discontinuous phase transition when the threshold is small and the average degree of the network is large, while in other cases the NCOT model displays a continuous phase transition.
We study the relationship between the partially synchronous state and the coupling structure in general dynamical systems. Our results show that, on the contrary to the widely accepted concept, topological symmetry in a coupling structure is the suff
icient condition but not the necessary condition. Furthermore, we find the necessary and sufficient condition for the existence of the partial synchronization and develop a method to obtain all of the existing partially synchronous solutions for all nonspecific dynamics from a very large number of possible candidates.
Using the properties of SDSS DR7 QSOs catalog from Shen et al., the Baldwin effect, its slope evolution, the underlying drive for a large sample of 35019 QSOs with reliable spectral analysis are investigated. We find that the Baldwin effect exists in
this large QSOs sample, which is almost the same in 11 different redshift bins, up to $zsim 5$. The slope is -0.238 by the BCES (civ EW depends on the continuum), -0.787 by the BCES bisector. For 11 redshift-bins, there is an increasing of the Baldwin effect slope from $zsim1.5$ to $zsim2.0$. From $zsim2.0$ to $zsim5.0$, the slope change is not clear considering their uncertainties or larger redshift bins. There is a strong correlation between the rest-frame civ EW and civ-based mbh while the relation between the civ EW and mgii-based mbh is very weak. With the correction of civ-based mbh from the civ blueshift relative to mgii, we suggest that this strong correlation is due to the bias of the civ-based mbh, with respect to that from the mgii line. Considering the mgii-based mbh, a medium strong correlation is found between the civ EW and the Eddington ratio, which implies that the Eddington ratio seems to be a better underlying physical parameter than the central black hole mass.
$Range$ and $load$ play keys on the problem of attacking on links in random scale-free (RSF) networks. In this Brief Report we obtain the relation between $range$ and $load$ in RSF networks analytically by the generating function theory, and then giv
e an estimation about the impact of attacks on the $efficiency$ of the network. The analytical results show that short range attacks are more destructive for RSF networks, and are confirmed numerically. Further our results are consistent with the former literature (Physical Review E textbf{66}, 065103(R) (2002)).
