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Trajectories of units moving on networks are relevant for nonlinear dynamical systems as diverse as polymers, ocean drifters, and human mobility. Although RQA is a well-researched tool with applications in many areas, it has rarely been…

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of…

Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…

Recurrence rate, determinism, average line length, and entropy of line lengths are measures of complexity in recurrence quantification analysis, that help to understand the structure, predictability and complexity of dynamical systems. In…

Steady technological advances and recent milestones such as intercontinental quantum communication and the first implementation of medium-scale quantum networks are paving the way for the establishment of the quantum internet, a network of…

Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space…

We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

Quantum systems exhibit recurrence phenomena after equilibration, but it is a difficult task to evaluate the recurrence time of a quantum system because it drastically increases as the system size increases (usually double-exponential in…

We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…

We investigate the dissipative dynamics of quantum population and coherence among different network topologies of a quantum network using a quantum spin model coupled to a thermal bosonic reservoir. Our study proceeds in two parts. First,…

In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…

We analyze how the performance of a quantum-repeater network depends on the protocol employed to distribute entanglement, and we find that the choice of repeater-to-repeater link protocol has a profound impact on communication rate as a…

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…

Spatially-resolved photon counting of a twin beam performed by an iCCD camera allows for versatile tailoring the properties of the beams formed by parts of the original twin beam. Dividing the idler beam of the twin beam into three…

Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely…

We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…