title: Contraction stability and transverse stability of synchronization in complex networks.
abstract: We consider discrete dynamical networks, and analytically demonstrate the relation between transverse stability in the Milnor sense and contraction stability, the stability for synchronous manifolds obtained via the partial contraction principle. By contraction for a system, we mean that initial conditions or temporary disturbances are forgotten exponentially fast, so that all trajectories of this system converge to a unique trajectory. In addition, synchronization of star-shaped complex networks is investigated via the partial contraction principle. This example further verifies the interrelation between contraction and transverse stability.
authors.affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.
authors.forename: Kezan
authors.initials: K
authors.lastname: Li
authors.forename: Michael
authors.initials: M
authors.lastname: Small
authors.forename: Xinchu
authors.initials: X
authors.lastname: Fu