Synchronizing network systems in the presence of limited resources via edge snapping

In this work, we propose a multilayer control protocol for the synchronization of network dynamical systems under limited resources. In addition to the layer where the interactions of the system take place, i.e., the backbone network, we propose a second, adaptive layer, where the edges are added or removed according to the edge snapping mechanism. Different from classic edge snapping, the inputs to the edge dynamics are modified to cap the number of edges that can be activated. After studying the local stability of the overall network dynamics, we illustrate the effectiveness of the approach on a network of Rössler oscillators and then show its robustness in a more general setting, exemplified with a model of the Italian high-voltage power grid

A network-based structure-preserving dynamical model for the study of cascading failures in power grids

In this work we show that simple classic models of power grids, albeit frequently utilized in many applications, may not be reliable for investigating cascading failures problems. For this purpose, we develop a novel model, based on a structure-preserving approach, to obtain a network-based description of a power grid, where nodes correspond to generators and buses, while the links correspond to the physical lines connecting them. In addition, we also consider classic voltage and frequency protection mechanisms for lines and buses. Considering the Italian power grid as a case study of interest, we then investigate the propagation of an initial failure of any line of the power system, and compare the predicted impact of the failure according to different assumptions in the model such as the presence or absence of protection mechanisms and a simplified description of the system dynamics. In particular, it can be observed that more realistic models are crucial to determine the size of the cascading failure, as well as the sequence of links that may be involved in the cascade

Analysis of remote synchronization in complex networks

A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs [Bergner et al., Phys. Rev. E 85, 026208 (2012)]. We show the existence of a more general dynamical state of remote synchronization in arbitrary networks of coupled oscillators. This state is characterized by the synchronization of pairs of nodes that are not directly connected via a physical link or any sequence of synchronized nodes. This phenomenon is almost negligible in networks of phase oscillators as its underlying mechanism is the modulation of the amplitude of those intermediary nodes between the remotely synchronized units. Our findings thus show the ubiquity and robustness of these states and bridge the gap from their recent observation in simple toy graphs to complex networks

The Master Stability Function for Synchronization in Simplicial Complexes

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks of coupled dynamical systems, where the graph links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework that allows to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We consider the most general ensemble of identical dynamical systems, organized on the nodes of a simplicial complex, and interacting through synchronization-non-invasive coupling function. The simplicial complex can be of any dimension, meaning that it can account, at the same time, for pairwise interactions, three-body interactions and so on. In such a broad context, we show that complete synchronization exists as an invariant solution, and we give the necessary condition for it to be observed as a stable state in terms of a Master Stability Function. This generalizes the existing results valid for pairwise interactions (i.e. graphs) to the case of complex systems with the most general possible architecture. Moreover, we show how the approach can be simplified for specific, yet frequently occurring, instances, and we verify all our theoretical predictions in synthetic and real-world systems. Given the completely general character of the method proposed, our results contribute to the theory of dynamical systems with many-body interactions and can find applications in an extremely wide range of practical cases

Stability of Synchronization in Simplicial Complexes

Networks with higher order interactions, relevant to social groups, ecosystems and human brain, require new tools and instruments for their analysis. Gambuzza et al. propose an analytical approach which allows to find conditions for stable synchronization in many-body interaction networks

Calcitonin, as SMS 201-995, ameliorates the VIPoma syndrome.

A 72-year-old woman was referred to our hospital for diarrhea, abdominal and back pain, weight loss, low serum potassium level. Pathological findings and high circulating Vasoactive Intestinal Peptide (VIP) levels allowed us to diagnose "VIPoma syndrome". The patient underwent a treatment with SMS 201-995 with improvement of symptomatology and reduction of circulating VIP levels. After a wash-out period the patient was treated with salmon calcitonin with a net improvement of diarrhea, normalization of potassium serum level and reduction of VIP level. The symptomatology recurred after calcitonin withdrawal. These data confirm the effectiveness of SMS 201-995 in the VIPoma syndrome and suggest that calcitonin may ameliorate symptomatology and reduce circulating VIP level in patients with VIPoma tumor

Intra-layer synchronization in multiplex networks

We study synchronization of N oscillators indirectly coupled through a medium which is inhomogeneous and has its own dynamics. The system is formalized in terms of a multilayer network, where the top layer is made of disconnected oscillators and the bottom one, modeling the medium, consists of oscillators coupled according to a given topology. The different dynamics of the medium and the top layer is accounted for by including a frequency mismatch between them. We show a novel regime of synchronization as intra-layer coherence does not necessarily require inter-layer coherence. This regime appears under mild conditions on the bottom layer: arbitrary topologies may be considered, provided that they support synchronization of the oscillators of the medium. The existence of a density-dependent threshold as in quorum-sensing phenomena is also demonstrated