Abstract
A new measure for the characterization of interconnected dynamical systems coupling is proposed. The method is based on the representation of time series as weighted cross-visibility networks. The weights are introduced as the metric distance between connected nodes. The structure of the networks, depending on the coupling strength, is quantified via the entropy of the weighted adjacency matrix. The method has been tested on several coupled model systems with different individual properties. The results show that the proposed measure is able to distinguish the degree of coupling of the studied dynamical systems. The original use of the geodesic distance on Gaussian manifolds as a metric distance, which is able to take into account the noise inherently superimposed on the experimental data, provides significantly better results in the calculation of the entropy, improving the reliability of the coupling estimates. The application to the interaction between the El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole and to the influence of ENSO on influenza pandemic occurrence illustrates the potential of the method for real-life problems.
Highlights
The synchronization between systems connected through some form of coupling is a common phenomenon occurring in a wide variety of fields, like physics, engineering, biology, physiology, secure communication, environmental sciences, etc
By using the each noisycycle periodic signals mapped random representation can be obtained by connecting cycles for which the phase space distance is less than a networks, while chaotic time series lead to complex networks exhibiting small-world and scale-free predefined value
The new method of weighted cross-visibility networks has been applied to time series for the
Summary
The synchronization between systems connected through some form of coupling is a common phenomenon occurring in a wide variety of fields, like physics, engineering, biology, physiology, secure communication, environmental sciences, etc. An analytical measure based on the time rate of information flowing from one series to the other was proposed in [22], with the advantage that the resulting formula involves only commonly used statistics. A detailed evaluation of several synchronization measures is reported in [23] Most of these methods are based the assumption that a stronger coupling leads to a stronger synchronization. As noticed in [23], different systems may have different behaviors during their transition to synchronization and the Lyapunov exponent is not always strictly monotonic This assumption remains a practical method to evaluate the effect of the coupling strength variations especially for real-life data. We are proposing a measure that is based on transforming the time series into graphs by means of the “cross-visibility networks” (CVN) method [24]. Conclusions and indications of further developments are the subject of the last section of the paper
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