Effect of spatial distribution on the synchronization in rings of coupled oscillators

In this paper, the effects of spatial distribution of coupling on the synchronizability are explored in a ring of diffusively coupled oscillators. We find that the inhomogeneity and spatial arrangements of coupling strength have great impacts on the synchronizability. When the inhomogeneous coupling constants are spatially rearranged, the eigenvalues λ 2 (the second largest eigenvalue of the coupling matrixes) for all possible spatial arrangements, which may describe the synchronizability of coupled oscillators, obey a log-normal distribution. The spatial arrangement of period 1 achieves the best synchronizability while that of period 2 has the worst one. In addition, the regimes of the effects of spatial distribution on synchronizability are analyzed by a ring of coupled Rossler systems. The spatial rearrangement of coupling has meaningful applications in the manipulation of self- organization for coupled systems.