Numerical Analysis on behavior of coupled maps on regular ring lattice with high degrees*

Behavior of coupled dynamical systems strongly depends on network structures, i.e. how dynamical systems connect with each other. We here numerically show what happens when the degree (K) of regular ring lattice increases. In the ring lattice, it is known that the clustering coefficient (C) is 3(K — 2)/4(K — 1). This predicts that C becomes about 3/4, when K is sufficiently large. However, we find that this is not satisfied when K is large, because of the periodic boundary condition of the ring lattice. We further investigate how the change in C of the ring lattice affects behavior of coupled dynamical systems on the ring lattice.