Resilience of the slow component in timescale-separated synchronized oscillators.

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently.

Stability of Kuramoto networks subject to large and small fluctuations from heterogeneous and spatially correlated noise.

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise. In this article, we focus on the assessment of fluctuations resulting from heterogeneous and spatially correlated noise inputs on Kuramoto model networks.

Evolution of Robustness in Growing Random Networks.

Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time.

Faster network disruption from layered oscillatory dynamics.

Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium, and, depending on the direction and the amplitude of the excursion, it might undergo a transition to another equilibrium. It was recently demonstrated [M.

Reconstructing network structures from partial measurements.

The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict the dynamics, or to better understand inter-agent processes. In many important and interesting situations, the network structure is not known, however, and previous investigations have shown how it may be inferred from complete measurement time series on each and every agent.

Periodic coupling inhibits second-order consensus on networks.

Consensus algorithms on networks have received increasing attention in recent years for various applications, ranging from distributed decision making to multivehicle coordination. In particular, second-order consensus models take into account the Newtonian dynamics of interacting physical agents. For this model class, we uncover a mechanism inhibiting the formation of collective consensus states via rather small time-periodic coupling modulations.

The key player problem in complex oscillator networks and electric power grids: Resistance centralities identify local vulnerabilities.

Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power grids and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony.

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties.

In modern electric power networks with fast evolving operational conditions, assessing the impact of contingencies is becoming more and more crucial. Contingencies of interest can be roughly classified into nodal power disturbances and line faults. Despite their higher relevance, line contingencies have been significantly less investigated analytically than nodal disturbances.

Global robustness versus local vulnerabilities in complex synchronous networks.

In complex network-coupled dynamical systems, two questions of central importance are how to identify the most vulnerable components and how to devise a network making the overall system more robust to external perturbations. To address these two questions, we investigate the response of complex networks of coupled oscillators to local perturbations. We quantify the magnitude of the resulting excursion away from the unperturbed synchronous state through quadratic performance measures in the angle or frequency deviations.

Noise-induced desynchronization and stochastic escape from equilibrium in complex networks.

Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, they can push the system from an initial stable equilibrium point, over a nearby saddle point, outside of the basin of attraction of the stable point.

Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices.

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbations, the response of synchronous states depends on the eigenvalues of the stability matrix of the unperturbed dynamics, as well as on its eigenmodes via their overlap with the perturbation vector.

The size of the sync basin revisited.

In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated to quantify the non-linear stability of fixed points of dynamical systems through the relative volumes of the associated basins of attraction [Wiley et al.