Twin surrogates to test for complex synchronisation

¹ Nonlinear Dynamics, Institute of Physics, University of Potsdam Potsdam, Germany
² Cognitive Psychology, Department of Psychology, University of Potsdam Potsdam, Germany

Corresponding author: thiel@agnld.uni-potsdam.de

Received: 2 March 2006
Accepted: 24 June 2006

Abstract

We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rössler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems.