title: Various oscillation patterns in phase models with locally attractive and globally repulsive couplings.
abstract: We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.
authors.affiliation: Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0020, Japan.
authors.forename: Katsuhiko
authors.initials: K
authors.lastname: Sato
authors.affiliation: Graduate School of Simulation Studies, University of Hyogo, Kobe 650-0047, Japan.
authors.forename: Shin-ichiro
authors.initials: S
authors.lastname: Shima