Network analyses of nonlinear time series and complex spatial structures

A test for nonlinearity based on network measures of recurrence networks is proposed and compared to a powerful measure for nonlinearity, namely the nonlinear prediction error. Simulated time series from the Lorenz System and light curves from Active Galactic Nuclei are studied. The new test based on networks shows similar discrimination power. Both tests detect induced phase correlations in so-called surrogate data produced by two established algorithms. In a second part, two promising applications of network analysis to complex plasma clusters are described. The detection of vertical strings with the aid of a community-finding algorithm has proven an elegant way of examining stable units in complex structures. Network analysis also enables a throughout study of the global structure of the clusters. For the relatively small clusters of about 60 particles a significant diverence between the well-studied case of nonrotating clusters and dynamically driven clusters is demonstrated.