title: Synchronization and spatiotemporal patterns in coupled phase oscillators on a weighted planar network.
abstract: To reveal the relation between network structures found in two-dimensional biological systems, such as protoplasmic tube networks in the plasmodium of true slime mold, and spatiotemporal oscillation patterns emerged on the networks, we constructed coupled phase oscillators on weighted planar networks and investigated their dynamics. Results showed that the distribution of edge weights in the networks strongly affects (i) the propensity for global synchronization and (ii) emerging ratios of oscillation patterns, such as traveling and concentric waves, even if the total weight is fixed. In-phase locking, traveling wave, and concentric wave patterns were, respectively, observed most frequently in uniformly weighted, center weighted treelike, and periphery weighted ring-shaped networks. Controlling the global spatiotemporal patterns with the weight distribution given by the local weighting (coupling) rules might be useful in biological network systems including the plasmodial networks and neural networks in the brain.
authors.affiliation: Department of Electrical Engineering and Bioscience, Waseda University, Tokyo 169-8555, Japan. ykagawa@aoni.waseda.jp
authors.forename: Yuki
authors.initials: Y
authors.lastname: Kagawa
authors.forename: Atsuko
authors.initials: A
authors.lastname: Takamatsu