Related papers: Reliability of Coupled Oscillators II: Larger Netw…
We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phase-oscillator's natural…
This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled…
Modern societies crucially depend on the robust supply with electric energy. Blackouts of power grids can thus have far reaching consequences. During a blackout, often the failure of a single infrastructure, such as a critical transmission…
The production network under examination consists of a number of workstations. Each workstation is a parallel configuration of machines performing the same kind of tasks on a given part. Parts move from one workstation to another and at…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
In a cascading power transmission outage, component outages propagate non-locally, after one component outages, the next failure may be very distant, both topologically and geographically. As a result, simple models of topological contagion…
We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
Networks - collections of interacting elements or nodes - abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions,…
Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…
In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their…
In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…
While phase oscillators are often used to model neuronal populations, in contrast to the Kuramoto paradigm, strong interactions between brain areas can be associated with loss of synchrony. Using networks of coupled oscillators described by…
The stability of complex networks, from power grids to biological systems, is crucial for their proper functioning. It is thus important to control such systems to maintain or restore their stability. Traditional approaches rely on…
Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node. Here, we reveal the mechanism…
Nowadays, the consequences of failure and downtime of distributed systems have become more and more severe. As an obvious solution, these systems incorporate protection mechanisms to tolerate faults that could cause systems failures and…