Title: Radial and circular synchronization clusters in extended starlike network of van der Pol oscillators,
Abstract: We consider extended starlike networks where the hub node is coupled with
several chains of nodes representing star rays. Assuming that nodes of the
network are occupied by nonidentical self-oscillators we study various forms of
their cluster synchronization. Radial cluster emerges when the nodes are
synchronized along a ray, while circular cluster is formed by nodes without
immediate connections but located on identical distances to the hub. By its
nature the circular synchronization is a new manifestation of so called remote
synchronization [Phys. Rev. E 85 (2012), 026208]. We report its long-range form
when the synchronized nodes interact through at least three intermediate nodes.
Forms of long-range remote synchronization are elements of scenario of
transition to the total synchronization of the network. We observe that the far
ends of rays synchronize first. Then more circular clusters appear involving
closer to hub nodes. Subsequently the clusters merge and, finally, all network
become synchronous. Behavior of the extended starlike networks is found to be
strongly determined by the ray length, while varying the number of rays
basically affects fine details of a dynamical picture. Symmetry of the star
also extensively influences the dynamics. In an asymmetric star circular
cluster mainly vanish in favor of radial ones, however, long-range remote
synchronization survives.