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The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
The synchronization of power generators is an important condition for the proper functioning of a power system, in which the fluctuations in frequency and the phase angle differences between the generators are sufficiently small when…
Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with three-body interaction.…
In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or…
This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators…
Power systems are subject to fundamental changes due to the increasing infeed of decentralised renewable energy sources and storage. The decentralised nature of the new actors in the system requires new concepts for structuring the power…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different…
The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
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…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds.…
In this work, we propose a control scheme for power grids subject to large perturbations that cause the failure of a node of the grid. Under such circumstances, the system may lose synchrony and, in addition, a cascade of line failures can…