Geometric signature of complex synchronisation scenarios
1 Potsdam Institute for Climate Impact Research - P.O. Box 60 12 03, 14412 Potsdam, Germany, EU
2 Department of Physics, Humboldt University - Newtonstr. 15, 12489 Berlin, Germany, EU
3 Stockholm Resilience Centre, Stockholm University - Kräftriket 2B, 11419 Stockholm, Sweden, EU
4 Institute for Complex Systems and Mathematical Biology, University of Aberdeen Aberdeen AB24 3FX, UK, EU
Received: 30 November 2012
Accepted: 23 April 2013
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the coupling strength often leads to qualitative changes in the dynamics exhibiting different types of synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation (GS) between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, we show that the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful new indicator for the emergence of GS.
This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckmann et al. (EPL, 4 (1987) 973).
PACS: 05.45.Tp – Time series analysis / 05.45.Xt – Synchronization; coupled oscillators / 89.75.Hc – Networks and genealogical trees
© EPLA, 2013