arXiv subjects

Timoteo Carletti

Publications and source records attributed to Timoteo Carletti.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Navigation on Simplicial Complexes

The navigation time and optimal search strategies deriving from random dynamical processes on binary graphs have been extensively explored and analyzed, being of prominent interest in the network science field. In this work, we study an extension of these topological measures for simplicial complexes: a specific type of geometric and algebraic structures that encapsulates higher-order interactions. Here, the explorability analysis of simplicial complexes has been conducted in terms of the mean first passage times between nodes, i.e. the 0th-order simplices, with the inclusion of a long-range stochastic teleportation term modulated with respect to the local random walk hopping across the various dimensions. We also provide a perturbative approximation scheme recovering the modulation parameter between pure random walk and teleportation mode (for higher-order setting) acting as the expansion parameter.

cond-mat.stat-mech↗

arXiv2026

Diffusion-induced instabilities promote cooperation in eco-evolutionary networks

Understanding how cooperation persists despite the advantage of selfish behavior remains a central challenge in evolutionary dynamics. Classical models of public goods dilemmas predict dominance of defectors, yet natural and social systems often sustain cooperation. We study an eco-evolutionary public goods game on complex networks where cooperators and defectors diffuse at different rates. When the isolated system is in a defector-dominated coexistence regime, faster dispersal of defectors than cooperators leads to a symmetry-breaking transition that produces localized clusters of cooperators. In heterogeneous networks, nodes with higher connectivity become significantly more likely to exhibit cooperative dominance. A degree-based mean-field reduction supports this result by showing that network connectivity controls an effective coupling strength proportional to node degree, thereby producing a bifurcation that separates defector-dominated and cooperative states. We also address why not all hubs become cooperative by means of a multistability analysis. These results reveal how asymmetric mobility and heterogeneous connectivity jointly promote cooperation in structured populations.

physics.soc-ph↗

arXiv2026

Swarming and Opinion Dynamics

Collective dynamics in multi-agent systems provide a powerful framework for understanding how coherent group-level patterns can emerge from simple interactions between individuals. Such phenomena are observed in many natural and artificial systems, including animal groups, robotic swarms, and distributed decision-making processes. In many situations, agents are not only characterized by their spatial motion, but also by internal states, e.g., opinions or preferences, which evolve through interactions with peers. Understanding how these internal states influence collective motion, and how spatial organization in turn affects internal dynamics, remains an important challenge. In this work, we propose a model of coupled collective motion and opinion dynamics. The spatial dynamics are governed by attraction--repulsion interactions, while the internal dynamics are described by a Deffuant-type opinion model. Our results show that the confidence threshold of the opinion dynamics plays a key role in controlling the number of opinion clusters, whereas the strength of the opinion-dependent spatial attraction determines whether these clusters spatially merge or remain separated. In addition, for the full-consensus state, we derive the expression for the radius of the stationary swarm distribution when a nonlinear attraction kernel is used, using a semi-analytical approach. The proposed framework may be useful for studying collective decision-making, animal group behavior, and coordination strategies in swarm robotics.

nlin.AO↗

arXiv2026

Higher-order interactions for controlling time-delayed Kuramoto model

We propose a framework for controlling the collective dynamics of the time-delayed Kuramoto model based on a delay-free, higher-order approximation of the delayed interactions. By applying the Ott--Antonsen ansatz and the second-order averaging method to the resulting higher-order Kuramoto model, we obtain a one-dimensional reduced equation for the order parameter dynamics. Numerical simulations demonstrate that the higher-order approximation predicts the dynamics of the original delayed system more accurately than the conventional pairwise approximation and enables the realization of bistability and intermediate synchronization states. Our results demonstrate the effectiveness of higher-order interpretations of time delays for the control of oscillator networks with time-delayed interactions.

nlin.AO↗

arXiv2026

Sandpile Models on complex networks

We investigate the sandpile model on complex networks by developing a branching-process framework that explicitly incorporates dissipation during avalanche propagation. Unlike classical branching descriptions, which assume conservative transport and locally tree-like independence, the present approach introduces grain-loss effects directly into the offspring distribution, yielding generalized generating functions for dissipative avalanche dynamics. In the dissipative regime, avalanche-size distributions acquire exponential cutoffs while preserving topology-dependent scaling behavior. Numerical simulations confirm the theoretical predictions on sparse random networks and reveal systematic deviations in highly structured topologies. In particular, by using Holme-Kim clustered scale-free networks, we show that increasing clustering continuously lowers the avalanche exponent and enhances the probability of large cascades, demonstrating that short cycles generate strong correlations that invalidate the classical independent-branch approx imation. Surprisingly, trees also exhibit substantial deviations from power-law because low edge density and the abundance of leaves constrain avalanche propagation. These results show that dissipation, clustering, and sparse connectivity fundamentally reshape avalanche size distribution of the sandpile model on networks and establish quantitative limits for branching-process descriptions of avalanche dynamics.

cond-mat.stat-mech↗

arXiv2026

Synchronization of coupled wind turbines

In the context of renewable energies, wind energy appears as a sustainable alternative to address current environmental and energy challenges. This work studies the synchronization and stability of a network of wind turbines subjected to strong disturbances, by integrating a realistic modeling of wind variability by using the Ornstein-Uhlenbeck stochastic process. The dynamics of each wind turbine are described by a Kuramoto-type equation, while synchronization is analyzed through the time evolution of the phases. Stability is studied by analyzing the basin of attraction to the synchronous solution, namely the set of initial conditions leading to the stable synchronous state. Simulations carried out on various models ranging from an isolated wind turbine with constant power to an isolated wind turbine with variable wind power, reveal that the stability of the system is strongly influenced by inertia, damping, wind speed, wind fluctuation rate, correlation time, and coupling strength. Physically, these parameters control the balance between injected mechanical power, energy dissipation, grid-induced restoring forces, and the temporal structure of wind fluctuations, thereby determining the ability of the wind turbine to absorb perturbations and maintain synchronization under fluctuating wind conditions.

physics.soc-ph↗

arXiv2026

Model of Simplicial Complexes with dimension-wise preferential attachment

Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have brought to the fore the relevance of higher-order networks, namely structures allowing to encode for many-body interaction, differently from the pairwise case handled by networks. This novel research field opens new avenues of research with applications ranging from neurosciences to social sciences; there is thus a need for generative models of higher-order network capable to reproduce features present in empirical data. In this work we present a model for growing simplicial complex rooted on a preferential attachment process acting dimension-wise, i.e., returning a power law distribution for the generalized degree of simplexes of different dimension.

cond-mat.stat-mech↗

arXiv2026

The role of asymmetric time delay and its structure in 1D swarmalators

Swarmalators are a class of coupled oscillators that simultaneously synchronize in both space and phase, providing a minimal model for systems ranging from biological microswimmers to robotic swarms. Time delay is ubiquitous in such systems, arising from finite signal propagation speeds and sensory processing lags, yet its structural form, whether symmetric or asymmetric, has received little attention. Here, we study a one-dimensional swarmalator model with asymmetric time delay, in which the delay enters only the self-interaction terms of the spatial and phase dynamics, breaking the symmetry assumed in prior work. We identify various collective states such as async, static phase wave, static {\pi}, and active {\pi}, and derive analytical stability boundaries for each as a function of the coupling parameters and delay. Our analysis reveals that the asymmetric delay structure fundamentally reshapes the collective phase diagram: in particular, for the asymmetric delay models, increasing the delay systematically expands the active {\pi} state at the expense of other ordered states, in contrast to the symmetric delay model, which more strongly promotes the presence of unsteady states that are generally not well ordered. By providing closed-form stability conditions validated against numerical simulations, our work establishes that the internal structure of the delay, not merely its magnitude, is a decisive factor in determining the emergent collective behavior of swarmalator populations.

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

Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane

We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynamical systems (DSs). Morphologically, they are characterized by a branch and a soma with several vertices (arms) and sometimes with multiple periodicities. A bunch of infinite astrocytes emerge through their branches from a region, in general, of low periodicity. Astrocytes are embedded in a quasiperiodic-chaotic scenario. The soma complexity (number of vertices) determines a kind of hierarchy of the astrocytes; moreover, bunches of subsequent structures from the astrocyte have been emphasized, revealing a self-similarity property. We conducted a detailed analysis in a Zeeman laser model, but we also observed astrocytes in many other DSs. The multiperiodicity exhibited by the astrocytes in their soma gives rise to harlequin dress-like patterns and tri-, quad-, and quint-critical points, which indicate the coexistence of different higher-order periodicities. In the concave borders of the soma, a doubling cascade of quint-points emerges as a bifurcation in the PP, defining regions of ordered sequences of higher periodicity in the route to chaos.

nlin.CD↗

arXiv2026

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↗

arXiv2026

Spectral Higher-Order Neural Networks

Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures have been also designed that move beyond pairwise interactions, so as to account for higher-order couplings among computing neurons. Higher-order networks are however usually deployed as augmented graph neural networks (GNNs), and, as such, prove solely advantageous in contexts where the input exhibits an explicit hypergraph structure. Here, we present Spectral Higher-Order Neural Networks (SHONNs), a new algorithmic strategy to incorporate higher-order interactions in general-purpose, feedforward, network structures. SHONNs leverages a reformulation of the model in terms of spectral attributes. This allows to mitigate the common stability and parameter scaling problems that come along weighted, higher-order, forward propagations.

cs.LG↗

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

Synchronization of higher-dimensional Kuramoto oscillators on networks: from scalar to matrix-weighted couplings

The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by interacting through a sinusoidal coupling. In this work, we propose a d-dimensional generalization in which oscillators are represented as unit vectors on the (d-1)-sphere and interact through a matrix-weighted network (MWN), a recently introduced framework where links are endowed with a matrix weight instead of a scalar one. We derive necessary conditions for global synchronization via a Master Stability Function approach: the existence of a synchronous solution requires identical frequency matrices across nodes and, in the MWN case, a coherence condition on the network structure. Through a suitable change of variables, the stability analysis reduces the full Nd-dimensional problem to a family of d-dimensional eigenvalue problems, each one parametrized by the eigenvalue of a suitable scalar weighted Laplacian, showing that the synchronous solution is locally stable for any positive coupling strength K on any connected network. Analytical results are complemented by numerical simulations.

cond-mat.stat-mech↗

arXiv2026

Topology and higher-order global synchronization on directed and hollow simplicial and cell complexes

Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating higher-order topological dynamics where dynamical variables are not only associated with nodes, but also with edges, triangles, and higher-order simplices and cells. Global Topological Synchronization (GTS) refers to the dynamical state in which identical oscillators associated with higher-dimensional simplices and cells oscillate in unison. On standard unweighted and undirected complexes this dynamical state can be achieved only under strict topological and combinatorial conditions on the underlying discrete support. In this work we consider generalized higher-order network representations including directed and hollow complexes. Based on an in depth investigation of their topology defined by their associated algebraic topology operators and Betti numbers, we determine under which conditions GTS can be observed. We show that directed complexes always admit a global topological synchronization state independently of their topology and structure. However, we demonstrate that for directed complexes this dynamical state cannot be asymptotically stable. While hollow complexes require more stringent topological conditions to sustain global topological synchronization, these topologies can favor both the existence and the stability of global topological synchronization with respect to undirected and unweighted complexes.

physics.soc-ph↗

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↗

arXiv2026

Turing patterns in Matrix-Weighted Networks

Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights, possibly complemented by cross-diffusion terms that are homogeneous across links. In this work, we investigate the emergence of Turing patterns on Matrix Weighted Networks (MWNs), a recently introduced framework in which each edge is associated with a matrix weight. Focusing on the class of coherent MWNs, we provide a novel characterization of coherence in terms of node-dependent orthonormal matrices, showing that link transformations can be written as relative rotations between nodes. This representation allows us to deal with coherent MWNs of any size and to introduce an orthonormal change of variables capable to reduce diffusion on a coherent MWN to diffusion on a standard weighted network with scalar weights. Building on this, we extend the classical Turing instability analysis to MWNs and derive the conditions under which a homogeneous equilibrium of the local dynamics loses stability due to matrix-weighted diffusion. Moving beyond the dimensional constraints of previous approaches, our results show how network topology, scalar weights, and inter-node transformations jointly shape pattern formation, and provide a constructive framework to analyze and design Turing patterns on matrix-weighted and higher-order networked systems.

cond-mat.stat-mech↗

arXiv2026

Random Walks Across Dimensions: Exploring Simplicial Complexes

We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrary large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher order simplices. Optimal search strategies in presence of stochastic teleportation are addressed and the peculiar interplay of noise with higher order structures unraveled.

cond-mat.stat-mech↗