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Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
Networks of coupled oscillators are some of the most studied objects in the theory of dynamical systems. Two important areas of current interest are the study of synchrony in highly disordered systems and the modeling of systems with…
The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution although these are often experimentally inaccessible. Here we propose a theory for revealing…
Collective behavior among coupled dynamical units can emerge in various forms as a result of different coupling topologies as well as different types of coupling functions. Chimera states have recently received ample attention as a…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…
Multi-agent systems exhibit complex behaviors that emanate from the interactions of multiple agents in a shared environment. In this work, we are interested in controlling one agent in a multi-agent system and successfully learn to interact…
A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur…
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…
We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of…
An important open problem in Human Behaviour is to understand how coordination emerges in human ensembles. This problem has been seldom studied quantitatively in the existing literature, in contrast to situations involving dual interaction.…
We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type…
Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare such systems and to…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…