title: Synchronization in asymmetrically coupled networks with node balance.
abstract: We study global stability of synchronization in asymmetrically connected networks of limit-cycle or chaotic oscillators. We extend the connection graph stability method to directed graphs with node balance, the property that all nodes in the network have equal input and output weight sums. We obtain the same upper bound for synchronization in asymmetrically connected networks as in the network with a symmetrized matrix, provided that the condition of node balance is satisfied. In terms of graphs, the symmetrization operation amounts to replacing each directed edge by an undirected edge of half the coupling strength. It should be stressed that without node balance this property in general does not hold.
authors.affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA. ibelykh@mathstat.gsu.edu
authors.forename: Igor
authors.initials: I
authors.lastname: Belykh
authors.forename: Vladimir
authors.initials: V
authors.lastname: Belykh
authors.forename: Martin
authors.initials: M
authors.lastname: Hasler
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009435:Synaptic Transmission / Q000502:physiology*; D013997:Time Factors