arXiv subjects

Riccardo Muolo

Publications and source records attributed to Riccardo Muolo.

At least 19 recordsLinked to original sources

arXiv2026

Symmetry-based selection rules for higher-order interactions in coupled oscillators

Pairwise interactions among general nonlinear oscillators can be reduced, via phase reduction, to a Kuramoto-type phase coupling $\sin(- \theta_j+\theta_k )$. For higher-order interactions, multiple phase couplings exist -- such as $\sin(-2\theta_j+\theta_k+\theta_l )$ and $\sin(-\theta_j+2\theta_k-\theta_l)$. Since different nonpairwise coupling functions produce qualitatively different dynamics, it is important to understand which phase couplings should be included in coupled phase oscillator models. In this Letter, we establish selection rules for higher-order phase coupling functions. These selection rules, which can be applied without the need of explicit phase reduction, are solely based on the symmetry of the isolated oscillator velocity field and the $n$-body interaction functions. As phase reduction established the mechanistic basis for the Kuramoto model, our results provide a theoretical link between physical systems and higher-order phase models.

nlin.AO↗

arXiv2026

Classification of Chimera States via Fourier Analysis and Unsupervised Learning

Chimera states are among the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators. Many methods have been proposed to detect chimera states and to distinguish their different types. However, such methods often suffer from important limitations that prevent sufficiently precise classification. In this work, we overcome the issue by considering a method based on Fourier analysis to determine key signal characteristics such as amplitude, phase, and frequency, jointly with an unsupervised clustering step acting on normalized total variations, measures of local spatial changes of the above-mentioned dynamical features. The proposed method allows us to identify regions in parameter space returning chimera states, but also to further distinguish between the different types. The method is applied to a network of Rayleigh oscillators, which has been shown to exhibit a rich variety of dynamical patterns.

nlin.PS↗

arXiv2026

A robust method to identify chimera states

Chimera states are one of the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators. Despite extensive studies and numerous observations in different settings, the development of reliable and systematic methods to classify chimera states and distinguish them from other dynamical patterns remains a challenging task. Existing approaches are often limited in scope and lack robustness. In this work, we propose a method based on Fourier analysis combined with statistical classification to identify chimera behavior. The method is applied to a system of topological signals coupled via the Dirac operator, where it successfully captures the rich dynamical regimes exhibited by the model. We demonstrate that the proposed approach is robust with respect to variations in network topology and system parameters. Beyond the specific model considered, the framework provides a general and automated tool for distinguishing different dynamical regimes in complex systems.

nlin.PS↗

arXiv2026

On the efficiency of pairwise Hamiltonian control to desynchronize the higher-order Kuramoto model

Synchronization of coupled oscillators is observed in many natural and engineered systems and emerges due to the interactions within the system. It can be both beneficial, e.g., in power grids, and harmful, e.g., in epileptic seizures. In the latter case, efficient control methods to desynchronize the systems are crucial. Recent studies have shown that interactions are not always pairwise, but higher-order, i.e., many-body, and this greatly affects the dynamics. For instance, higher-order interactions increase the linear stability of synchronized states but simultaneously shrink their attraction basin, with potentially opposite effects on control methods. Here, we use a minimally invasive pairwise control based on Hamiltonian control theory, and investigate its efficiency on phase oscillators with higher-order interactions. We show that, if the initial phases are close to the synchronized state, higher-order interactions make desynchronization more difficult to achieve. Otherwise, a non-monotonic effect appears: intermediate strengths of higher-order interactions impede desynchronization while larger ones facilitate it. In all cases, the control can desynchronize the system with a sufficient number of controlled nodes and intensity.

nlin.AO↗

arXiv2025

Collective dynamics of higher-order Vicsek model emerging from local conformity interactions

The Vicsek model is the paradigmatic framework for collective motion in systems of self-propelled particles. In its continuous-time formulation and most of its extensions, alignment arises from pairwise interactions among neighboring particles. In this work, we consider a model in which each particle assigns weights to its neighbors according to their alignment with the local consensus. This simple mechanism naturally yields a Vicsek-type model with pairwise and higher-order (i.e., nonpairwise) interactions. We analyze its collective dynamics through numerical simulations and approximate theory in the absence and presence of noise. The higher-order interactions generate a novel bidirectionally ordered phase, in which particles self-organize into oppositely moving groups. Moreover, we show that, depending on the relative strength of the pairwise and three-body interactions, the order-disorder transition can be either continuous or abrupt.

cond-mat.stat-mech↗

arXiv2025

Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay

We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the three-body interactions. Our findings reveal that time delays can be recast effectively as higher-order interactions, providing an insight into how coupling delays shape collective dynamics.

nlin.AO↗

arXiv2025

Time delay embeddings to characterize the timbre of musical instruments using Topological Data Analysis: a study on synthetic and real data

Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning, often overlook subtle characteristics of sound. Topological Data Analysis (TDA) can capture complex patterns, but its application to timbre has been limited, partly because it is unclear how to represent sound effectively for TDA. In this study, we investigate how different time delay embeddings affect TDA results. Using both synthetic and real audio signals, we identify time delays that enhance the detection of harmonic structures. Our findings show that specific delays, related to fractions of the fundamental period, allow TDA to reveal key harmonic features and distinguish between integer and non-integer harmonics. The method is effective for synthetic and real musical instrument sounds and opens the way for future works, which could extend it to more complex sounds using higher-dimensional embeddings and additional persistence statistics.

cs.SD↗

arXiv2025

Equivalence of additive and parametric pinning control protocols for systems of weakly coupled oscillators

Controlling the behavior of nonlinear systems on networks is a paramount task in control theory, in particular the control of synchronization, given its vast applicability. In this work, we focus on pinning control and we examine two different approaches: the first, more common in engineering applications, where the control is implemented through an external input (additive pinning); the other, where the parameters of the pinned nodes are varied (parametric pinning). By means of the phase reduction technique, we show that the two pinning approaches are equivalent for weakly coupled systems exhibiting periodic oscillatory behaviors. Through numerical simulations, we validate the claim for a system of coupled Stuart--Landau oscillators. Our results pave the way for further applications of pinning control in real-world systems.

math.OC↗

arXiv2025

Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks

The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex networks, allowing for both reciprocal or non-reciprocal links. The emergence of synchronization can be deduced by proving the linear stability of the limit cycle solution for the Stuart-Landau model; the linear coupling assumption allows for a complete analytical treatment of the problem, mostly because the linearized system turns out to be autonomous. In this work, we analyze Stuart-Landau oscillators coupled through nonlinear functions on both undirected and directed networks; synchronization now depends on the study of a non-autonomous linear system and thus novel tools are required to tackle the problem. We provide a complete analytical description of the system for some choices of the nonlinear coupling, e.g., in the resonant case. Otherwise, we develop a semi-analytical framework based on Jacobi-Anger expansion and Floquet theory, which allows us to derive precise conditions for the emergence of complete synchronization. The obtained results extend the classical theory of coupled oscillators and pave the way for future studies of nonlinear interactions in networks of oscillators and beyond.

nlin.PS↗

arXiv2025

Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators

The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators are derived from weakly interacting limit-cycle oscillators via phase reduction, this procedure does not necessarily yield the Kuramoto model or its higher-order extensions exactly for general limit-cycle oscillators and interaction functions, except in the special case of interacting Stuart-Landau oscillators. In this study, we artificially design optimal pairwise and higher-order interaction functions between limit-cycle oscillators, from which higher-order Kuramoto models can be exactly derived via phase reduction for arbitrary smooth limit-cycle oscillators. We validate the results through numerical simulations of FitzHugh-Nagumo oscillators, demonstrating that the collective synchronization dynamics predicted by the reduced higher-order Kuramoto models are realized. Control of the collective phase of the FitzHugh-Nagumo oscillators based on Ott-Antonsen reduction of the higher-order Kuramoto model is also demonstrated.

nlin.AO↗

arXiv2025

When higher-order interactions enhance synchronization: the case of the Kuramoto model

Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled oscillators, traditionally assuming pairwise interactions. However, many real-world systems exhibit group and many-body interactions, which can be effectively modeled through hypergraphs. Here we show that the effect of such higher-order interactions on synchronization is non-monotonic. Through a numerical study of higher-order Kuramoto models on random hypergraphs and on globally coupled systems, we find that the degree of synchronization reached from incoherent initial conditions is maximized at a small but nonzero higher-order coupling strength: weak higher-order interactions enhance synchronization when added to pairwise ones, whereas strong ones work against it, in line with earlier reports of reduced basins and of cluster states. We further show, through a cost-constrained allocation analysis, that under a constrained budget for interactions a mixed allocation of pairwise and higher-order couplings consistently achieves higher synchronization than relying on either type alone. These findings clarify the role of higher-order interactions in shaping collective dynamics and point to design principles for optimizing synchronization in complex systems.

nlin.AO↗

arXiv2025

Synchronization of Dirac-Bianconi driven oscillators

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network theory addresses this by considering variables defined on nodes, links, triangles, and higher-order simplices, called topological signals (or cochains). Moreover, topological signals of different dimensions can interact through the Dirac-Bianconi operator, which allows coupling between topological signals defined, for example, on nodes and links. Such interactions can induce various dynamical behaviors, for example, periodic oscillations. The oscillating system consists of topological signals on nodes and links whose dynamics are driven by the Dirac-Bianconi coupling, hence, which we call it Dirac-Bianconi driven oscillator. Using the phase reduction method, we obtain a phase description of this system and apply it to the study of synchronization between two such oscillators. This approach offers a way to analyze oscillatory behaviors in higher-order networks beyond the node-based paradigm, while providing a ductile modeling tool for node- and edge-signals.

nlin.PS↗

arXiv2025

Flutter Suppression Enhancement in Coupled Nonlinear Airfoils with Intermittent Mixed Interactions

Flutter suppression facilitates the improvement of structural reliability to ensure the flight safety of an aircraft. In this study, we propose a novel strategy for enlarging amplitude death (AD) regime to enhance flutter suppression in two coupled identical airfoils with structural nonlinearity. Specifically, we introduce an intermittent mixed coupling strategy, i.e., a linear combination of intermittent instantaneous coupling and intermittent time-delayed coupling between two airfoils. Numerical simulations are performed to reveal the influence mechanisms of different coupling scenarios on the dynamical behaviors of the coupled airfoil systems. The obtained results indicate that the coupled airfoil systems experience the expected AD behaviors within a certain range of the coupling strength and time-delayed parameters. The continuous mixed coupling favors the onset of AD over a larger parameter set of coupling strength than the continuous purely time-delayed coupling. Moreover, the presence of intermittent interactions can lead to a further enlargement of the AD regions, that is, flutter suppression enhancement. Our findings support the structural design and optimization of an aircraft wing for mitigating the unwanted aeroelastic instability behaviors.

nlin.CD↗

arXiv2025

Chimera states on m-directed hypergraphs

Chimera states are synchronization patterns in which coherent and incoherent regions coexist in systems of identical oscillators. This elusive phenomenon has attracted significant interest and has been widely analyzed, revealing several types of dynamical states. Most studies involve reciprocal pairwise couplings, where each oscillator exerts and receives the same interaction from neighboring ones, thus being modeled via symmetric networks. However, real-world systems often exhibit non-reciprocal, non-pairwise (many-body) interactions. Previous studies have shown that chimera states are more elusive in the presence of non-reciprocal pairwise interactions, while they are easier to observe when the interactions are reciprocal and higher-order (many-body). In this work, we investigate the emergence of chimera states on non-reciprocal higher-order structures, called m-directed hypergraphs, which we compare with their corresponding networks, and we observe that some types of chimera states can emerge due to directionality, which had not been previously observed in its absence. We also compare the effect of non-reciprocal interactions between higher-order and pairwise couplings, and we find numerically that chimera states appear over a broader parameter range when considering higher-order interactions than in the corresponding network case, demonstrating the impact of directionality and the effect of higher-order interactions. Finally, the nature of phase chimeras has been further validated through phase reduction theory.

nlin.PS↗

arXiv2025

Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models

Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such as the Kuramoto model. Classically, the method has been applied in the case where the interactions are only pairwise (two-body). However, increasing evidence shows that interactions in real-world systems are not pairwise but higher-order, i.e., many-body. Although synchronization in higher-order systems has received much attention, analytical results are scarce because of the highly nonlinear nature of the framework. In this paper, we fill the gap by presenting a general theory of phase reduction for the case of higher-order interactions. We show that the higher-order topology is preserved in the phase reduced model at the first order and that only odd couplings have an effect on the dynamics when certain symmetries are present. Additionally, we show the power and ductility of the phase reduction approach by applying it to a population of Stuart-Landau oscillators with an all-to-all configuration and with a ring-like hypergraph topology; in both cases, only the analysis of the phase model can provide insights and analytical results.

nlin.AO↗

arXiv2024

Global Topological Dirac Synchronization

Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network display the same dynamics as received great attention in network theory. Here we propose and investigate Global Topological Dirac Synchronization on higher-order networks such as cell and simplicial complexes. This is a state where oscillators associated to simplices and cells of arbitrary dimension, coupled by the Topological Dirac operator, operate at unison. By combining algebraic topology with non-linear dynamics and machine learning, we derive the topological conditions under which this state exists and the dynamical conditions under which it is stable. We provide evidence of 1-dimensional simplicial complexes (networks) and 2-dimensional simplicial and cell complexes where Global Topological Dirac Synchronization can be observed. Our results point out that Global Topological Dirac Synchronization is a possible dynamical state of simplicial and cell complexes that occur only in some specific network topologies and geometries, the latter ones being determined by the weights of the higher-order networks

cond-mat.stat-mech↗

arXiv2024

What can PhD students and postdocs do to counter inequalities?

In this opinion article, we gathered some reflections and practical tips on what Early Stage Researchers do against inequalities in academia. This is the longer version of an opinion paper that was recently published on the website of the International Society for Optics and Photonics (spie.org), containing more details and suggestions.

physics.soc-ph↗

arXiv2024

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↗