We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying K > 2 coupled subsystems.

In this study we introduce two new nodeweighted difference measures on complex networks as a tool for climate model evaluation. The approach facilitates the quantification of a model's ability to reproduce the spatial covariability structure of climatological time series. We apply our methodology to compare the performance of a statistical and a dynamical regional climate model simulating the South American climate, as represented by the variables 2 m temperature, precipitation, sea level pressure, and geopotential height field at 500 hPa. For each variable, networks are constructed from the model outputs and evaluated against a reference network, derived from the ERA-Interim reanalysis, which also drives the models. We compare two network characteristics, the (linear) adjacency structure and the (nonlinear) clustering structure, and relate our findings to conventional methods of model evaluation.To set a benchmark, we construct different types of random networks and compare them alongside the climate model networks. Our main findings are: (1) The linear network structure is better reproduced by the statistical model statistical analogue resampling scheme (STARS) in summer and winter for all variables except the geopotential height field, where the dynamical model CCLM prevails. (2) For the nonlinear comparison, the seasonal differences are more pronounced and CCLM performs almost as well as STARS in summer (except for sea level pressure), while STARS performs better in winter for all variables.

Abstract. -Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled systems including different types of synchronisation such as phase, lag, generalised, or even complete synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation 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, 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 indicator for the emergence of generalised synchronisation.