Figure 1

The figure shows several examples illustrating the self-organized and driven phase synchronization. The examples are chosen to demonstrate the two different ways of obtaining synchronized clusters and the variety of clusters that are formed. All the figures show node versus node diagram for $N=N_C=50$. After an initial transient (about 2000 iterates) phase synchronized clusters are studied for $T=100$. The logistic map parameter $\mu =4$. The solid circles show that the two corresponding nodes are coupled and the open circles show that the corresponding nodes are phase synchronized. In each case the node numbers are reorganized so that nodes belonging to the same cluster are numbered consecutively. (a) shows an ideal self-organized phase synchronization for a scale-free network for $g(x)=x$ and $ϵ=0.15$. (b) An ideal driven phase synchronization for a scale-free network for $g(x)=x$ and $ϵ=0.85$. (c) Mixed behavior for a scale-free network for $g(x)=f(x)$ and $ϵ=0.61$. (d) A dominant driven behavior for a scale-free network for $g(x)=f(x)$ and $ϵ=0.87$. (e) A dominant self-organized behavior for 1D lattice with nearest neighbor couplings for $g(x)=x$ and $ϵ=0.14$. (f) An ideal driven behavior with several isolated nodes for 1D lattice with nearest neighbor couplings for $g(x)=f(x)$ and $ϵ=0.15$. The scale-free networks were generated starting with $N_0=1$ nodes and adding one node with $m=1$ couplings at each stage of the growth of the lattice with the probability of connecting to a node being proportional to the degree of the node (see Ref. 9 for details).Reuse & Permissions

Figure 2

The fraction of intracluster and intercluster couplings, $f_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}$ (solid line) and $f_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}$ (dashed line) are shown as a function of the coupling strength $ϵ$. (a) and (b) are for the scale-free network for $g(x)=x$ and $g(x)=f(x)$, respectively. (c) and (d) are for the 1D network with nearest neighbor couplings for $g(x)=x$ and $g(x)=f(x)$, respectively. The figures are obtained by averaging over 20 realizations of a network and 50 random initial conditions for each realization.Reuse & Permissions