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Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply…
Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…
We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal…
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the…
In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of…
Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record…
Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network…
Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent…
While most spatial data can be modeled with the assumption that distant points are uncorrelated, some problems require dependence at both far and short distances. We introduce a model to directly incorporate dependence in phenomena that…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
We present a study on the spatio-temporal pattern underlying the climate dynamics in various locations spread over India, including the Himalayan region, coastal region, central and northeastern parts of India. We try to capture the…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
We propose a data-driven framework to simplify the description of spatiotemporal climate variability into few entities and their causal linkages. Given a high-dimensional climate field, the methodology first reduces its dimensionality into…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
Unmeasured causal forces influence diverse experimental time series, such as the transcription factors that regulate genes, or the descending neurons that steer motor circuits. Combining the theory of skew-product dynamical systems with…