Dresden 2011 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Nonlinear Dynamics I
DY 17.2: Talk
Wednesday, March 16, 2011, 10:45–11:00, ZEU 255
Topological stability criteria for synchronized coupled systems of non-identical oscillators — •Anne-Ly Do1, Stefano Boccaletti2, and Thilo Gross1 — 1MPI for the Physics Complex Systems, Dresden, Germany — 2CNR Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy
Individual dynamical units that are coupled via an interaction network can synchronize spontaneously without central regulation. The propensity to synchronize depends on structural properties of the interaction network. The influence of certain network properties such as heterogeneity and diameter have extensively been studied, however sometimes with conflicting conclusions. This might indicate that beside global structural measures of the network also the actual local configuration plays a role that cannot be neglected. Here, we show that synchronization can only be achieved when the network obeys topological criteria that are independent of any statistical network measure. We analytically derive topological conditions for the stability of stationary and phase-locked states by constructing a graphical interpretation of Jacobi's signature criterion. Furthermore, we show that the proposed approach can be extended to an adaptive network version of the Kuramoto-model, in which the coupling topology co-evolves with the dynamics of the coupled units.