Twin surrogates to test for complex synchronisation

PACS. 05.45.-a – Nonlinear dynamics and chaos. PACS. 05.45.Tp – Time series analysis. PACS. 05.45.Xt – Synchronization; coupled oscillators. 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. Introduction. – The concepts of complex synchronisation and especially phase synchronisation (PS) have been intensively studied in recent years [1]. Indications of PS have been found in many laboratory and natural systems [2]. The corresponding studies are usually based on the computation of a measure which quantifies dependencies of the instantaneous phases of the time series. However, even though these measures may be normalised between