arXiv subjects

Lucia Valentina Gambuzza

Publications and source records attributed to Lucia Valentina Gambuzza.

13 recordsLinked to original sources

arXiv2025

Pinning control of chimera states in systems with higher-order interactions

Understanding and controlling the mechanisms behind synchronization phenomena is of paramount importance in nonlinear science. In particular, the emergence of chimera states, patterns in which order and disorder coexist simultaneously, continues to puzzle scholars, due to its elusive nature. Recently, it has been shown that higher-order (many-body) interactions greatly enhance the presence of chimera states, which are easier to be found and more persistent. In this work, we show that the higher-order framework is fertile not only for the emergence of chimera states, but also for its control. Via pinning control, a technique consisting in applying a forcing to a subset of the nodes, we are able to trigger the emergence of chimera states with only a small fraction of controlled nodes, at striking contrast with the case without higher-order interactions. We show that our setting is robust for different higher-order topologies and types of pinning control and, finally, we give a heuristic interpretation of the results via phase reduction theory. Our numerical and theoretical results provide further understanding on how higher-order interactions shape collective behaviors in nonlinear dynamics.

nlin.PS↗

arXiv2024

Taming Cluster Synchronization

Synchronization is a widespread phenomenon observed across natural and artificial networked systems. It often manifests itself by clusters of units exhibiting coincident dynamics. These clusters are a direct consequence of the organization of the Laplacian matrix eigenvalues into spectral localized blocks. We show how the concept of spectral blocks can be leveraged to design straightforward yet powerful controllers able to fully manipulate cluster synchronization of a generic network, thus shaping at will its parallel functioning. Specifically, we demonstrate how to induce the formation of spectral blocks in networks where such structures would not exist, and how to achieve precise mastering over the synchronizability of individual clusters by dictating the sequence in which each of them enters or exits the synchronization stability region as the coupling strength varies. Our results underscore the pivotal role of cluster synchronization control in shaping the parallel operation of networked systems, thereby enhancing their efficiency and adaptability across diverse applications.

nlin.CD↗

arXiv2024

Phase chimera states on non-local hyperrings

Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to study chimera states in systems of identical oscillators, non-locally coupled through pairwise interactions. Nevertheless, there is an increasing evidence, also supported by available data, that complex systems are composed by multiple units experiencing many-body interactions, that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a novel topology solely involving many-body, non-local and non-regular interactions, hereby named non-local d-hyperring, being (d+1) the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are "flattened" to pairwise ones, the chimera behavior is weaker and more elusive.

nlin.PS↗

arXiv2023

Multilayer control of synchronization and cascading failures in power grids

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 be triggered as an effect of the flow redistribution that activates the protection mechanisms equipped on each line of the grid. To devise a control action for addressing this problem, we adopt a multi-layer network-based description of the power grid that incorporates an overflow condition to model the possibility of cascading failures. The two other layers of the structure are devoted to the control, one implements the distributed proportional control law, and the other the integral control law. To exemplify the application of our model, we study the Italian high-voltage power grid for different parameters and topologies of the control layers.

eess.SY↗

arXiv2023

Reconstructing higher-order interactions in coupled dynamical systems

Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of coupled dynamical units, identifying both pairwise and higher-order interactions from the system time evolution. Our method works for any dynamics, and allows the reconstruction of both hypergraphs and simplicial complexes, either undirected or directed, unweighted or weighted. With two concrete applications, we show how the method can help understanding the ecosystemic complexity of bacterial systems, or the microscopic mechanisms of interaction underlying coupled chaotic oscillators.

physics.soc-ph↗

arXiv2022

Synchronization induced by directed higher-order interactions

Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for in networks with pairwise interactions, its effects in systems with higher-order interactions have not yet been explored as deserved. Here, we introduce the concept of M-directed hypergraphs, a general class of directed higher-order structures, which allow to investigate dynamical systems coupled through directed group interactions. As an application we study the synchronization of nonlinear oscillators on 1-directed hypergraphs, finding that directed higher-order interactions can destroy synchronization, but also stabilize otherwise unstable synchronized states.

nlin.AO↗

arXiv2022

Control of cascading failures in dynamical models of power grids

In this paper, we introduce a distributed control strategy to prevent dynamically-induced cascading failures in power grids. We model power grids using complex networks and nonlinear dynamics to provide a coarse-grained description of the electro-mechanical phenomena taking place on them (in particular, we use coupled swing equations) and restrict our analysis to cascades of line failures, i.e., failures due to power flows exceeding the maximum capacity of a line. We formulate a distributed control protocol relying on the same topology of the physical layer and apply it to several power grid models, including a small-size illustrative example with five nodes, the Italian high-voltage (380kV) power grid, and the IEEE 118-bus system. Our results indicate that the approach is capable of preventing cascading failures, either controlling each node of the network or a suitable subset of them.

eess.SY↗

arXiv2021

Distributed control of multi-consensus

We consider the problem of steering a multi-agent system to multi-consensus, namely a regime where groups of agents agree on a given value which may be different from group to group. We first address the problem by using distributed proportional controllers that implement additional links in the network modeling the communication protocol among agents and introduce a procedure for the optimal selection of them. Both the cases of single integrators and of second-order dynamics are taken into account and the stability for the multi-consensus state is studied, ultimately providing conditions for the gain of the controllers. We then extend the approach to controllers that either add or remove links in the original structure, by preserving eventually the weak connectedness of the resulting graph.

eess.SY↗

arXiv2021

Control technique for synchronization of selected nodes in directed networks

In this Letter we propose a method to control a set of arbitrary nodes in a directed network such that they follow a synchronous trajectory which is, in general, not shared by the other units of the network. The problem is inspired to those natural or artificial networks whose proper operating conditions are associated to the presence of clusters of synchronous nodes. Our proposed method is based on the introduction of distributed controllers that modify the topology of the connections in order to generate outer symmetries in the nodes to be controlled. An optimization problem for the selection of the controllers, which includes as a special case the minimization of the number of the links added or removed, is also formulated and an algorithm for its solution is introduced.

nlin.CD↗

arXiv2017

Indirect Long-range Interactions and Network Synchronization

The dynamical behavior of networked complex systems is shaped not only by the direct links among the units, but also by the long-range interactions occurring through the many existing paths connecting the network nodes. In this work, we study how synchronization dynamics is influenced by these long-range interactions, formulating a model of coupled oscillators that incorporates this type of interactions through the use of $d-$path Laplacian matrices. We study synchronizability of these networks by the analysis of the Laplacian spectra, both theoretically and numerically, for real-world networks and artificial models. Our analysis reveal that in all networks long-range interactions improve network synchronizability with an impact that depends on the original structure, for instance it is greater for graphs having a larger diameter. We also investigate the effects of edge removal in graphs with long-range interactions and, as a major result, find that the removal process becomes more critical, since also the long-range influence of the removed link disappears.

physics.soc-ph↗

arXiv2015

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 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.

nlin.CD↗

arXiv2014

Chimera states in time-varying complex networks

Chimera states have been recently found in a variety of different coupling schemes and geometries. In most cases, the underlying coupling structure is considered to be static, while many realistic systems display significant temporal changes in the pattern of connectivity. In this work, we investigate a time-varying network made of two coupled populations of Kuramoto oscillators, where the links between the two groups are considered to vary over time. As a main result, we find that the network may support stable, breathing and alternating chimera states. We also find that, when the rate of connectivity changes is fast, compared to the oscillator dynamics, the network may be described by a low-dimensional system of equations. Unlike in the static heterogeneous case, the onset of alternating chimera states is due to the presence of fluctuations, which may be induced either by the finite size of the network or by large switching times.

nlin.AO↗

arXiv2013

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. 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.

physics.soc-ph↗