Abstract
Abstract. Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches – recurrence plots and recurrence networks –, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period–chaos and even period–period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.
Highlights
Recurrence-based approaches have taken an important place in dynamical system analysis
recurrence plot (RP) were first introduced as a visualization of recurrent states of phase space trajectories (Eckmann et al, 1987), but enriched by different quantification techniques for characterizing dynamical properties, regime transitions, synchronization, and so on (Marwan et al, 2007)
We have shown that time series can be analyzed by complex networks by identifying the RP by the adjacency matrix of a network (Marwan et al, 2009; Donner et al, 2011), forming so-called recurrence networks (RNs)
Summary
Recurrence-based approaches have taken an important place in dynamical system analysis. Related approaches have been used for several decades The basis of this analysis is finding recurrent points on a trajectory in the phase space of a dynamical system. Transitions in the dynamics can be detected by different RP-based measures, which, in general, are very useful to study complex, real-world systems (Trulla et al, 1996; Marwan et al, 2002; Donges et al, 2011). In order to uncover their time-dependent behavior, RQA measures are often computed by applying a sliding window on the time series, which can be used to identify dynamical transitions, such as period–chaos transitions (Trulla et al, 1996) or chaos–chaos transitions (Marwan et al, 2002) Another popular method for analyzing complex systems is the complex network approach (Watts and Strogatz, 1998; Boccaletti et al, 2006). By choosing the critical point c as the recurrence threshold, we ensure that the RN will be connected by the smallest threshold possible
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