arXiv subjects

Melvyn Tyloo

Publications and source records attributed to Melvyn Tyloo.

At least 19 recordsLinked to original sources

arXiv2026

Steering the dynamics by controlling the temporal interaction network

Many real-world coupled dynamical systems have the interaction structure and strength that evolve or adapt over time. Here, we investigate how one can control the state of a system by tuning its temporal interaction network. We present a framework based on nonlinear optimal control, where one has control over the coupling matrix of a dynamical system. We show how to obtain the gradient of the Lagrangian function of the system using the adjoint method. We then focus on a linear time-variant system for which we illustrate the framework. Finally, we explore how the states at the nodes can be steered to target trajectories, by controlling the coupling matrix, imposing various constraint on its structure. The workflow presented here can be leveraged to steer the dynamics of systems with artificial or engineered interaction that is tunable.

nlin.AO↗

arXiv2026

Network Reconstruction in Consensus Algorithms with Hidden Agents

Reconstructing the parameters that encode the influence between model variables based on time-series measurements represents an outstanding question in the theory of complex network-coupled systems. Here, we propose a solution to this problem for a class of noisy leader-follower consensus algorithm, where one has access to measurements only from the followers but not from the leaders. Leveraging the directed Laplacian coupling of such systems, we present an autoregressive expansion of the observed dynamics which can be truncated at different orders, depending on the memory of the leaders. When their memory is short, this allows one to correctly reconstruct the full dynamical matrix with hidden leader agents, provided some additional assumption on the system to lift the degeneracy in the reconstruction. We illustrate and check the theory using numerical simulations for the cases of both a single and multiple hidden leaders.

eess.SY↗

arXiv2026

A Closed-loop Framework to Discriminate Models Using Optimal Control

Predicting the response of an observed system to a known input is a fruitful first step to accurately control the system's dynamics. Despite the recent advances in fully data-driven algorithms, the most interpretable way to reach this goal is through mechanistic mathematical modeling. Here, we leverage optimal control and propose a closed-loop iterative method to choose among a set of candidate models the one that most accurately predict an observed system. We assume that one has control over an input of the observed system and access to measurements of its response. Our approach is to identify the input control that maximally discriminates the response of the candidate models, allowing us to determine which model is best by comparing such responses with the observed data. We demonstrate our proposed framework in numerical simulations before applying it during an electrophysiology experiment, successfully discriminating between different models for photocurrents produced via opsin dynamics.

math.DS↗

arXiv2025

Open networks in discrete time: Passing vs blocking behavior

This paper presents a unified framework for analyzing the input-output behavior of discrete time complex networks viewed as open systems. Importantly, we focus on systems that are inherently modeled in discrete time-such as opinion dynamics, Markov chains, diffusion on networks, and population models-reflecting their natural formulation in many real-world contexts. By an open network, we mean one that is coupled to its environment, through both external signals that are received by designated input nodes and response signals that are released back into the environment via a separate set of output nodes. We develop a general framework for characterizing whether such networks amplify (pass) or suppress (block) the external inputs. Our approach combines the transfer function of the network with the discrete time controllability Gramian, using the H2-norm to quantify signal amplification. We introduce a computationally efficient network index based on the Gramian trace and eigenvalues, enabling scalable comparisons across network topologies. Application of our method to a broad set of empirical networks, spanning biological, technological, and ecological domains, uncovers consistent structural signatures associated with passing or blocking behavior. These findings shed light on how the network architecture and the particular selection of input and output nodes shape information flow in real-world systems, with broad implications for control, signal processing, and network design.

physics.soc-ph↗

arXiv2025

The Frequency Response of Networks as Open Systems

Many biological, technological, and social systems can be effectively described as networks of interacting subsystems. Typically, these networks are not isolated objects, but interact with their environment through both signals and information that is received by specific nodes with an input function or released to the environment by other nodes with an output function. An important question is whether the structure of different networks, together with the particular selection of input and output nodes, is such that it favors the passing or blocking of such signals. For a given network and a given choice of the input and output nodes, the H2-norm provides a natural and general quantification of the extent to which input signals, whether deterministic or stochastic, periodic or arbitrary, are amplified. We analyze a diverse set of empirical networks and find that many naturally occurring systems, such as food webs, signaling pathways, and gene regulatory circuits, are structurally organized to enhance the passing of signals; in contrast, the structure of engineered systems like power grids appears to be intentionally designed to suppress signal propagation.

eess.SY↗

arXiv2025

Predicting the response of structurally altered and asymmetrical networks

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we consider the challenging problem of multiplicative perturbations and asymmetrical interaction coupling. We introduce a framework to approximate the averaged response at each network node for general structural perturbations, including non-normal and asymmetrical ones. Our findings indicate that both the asymmetry and non-normality of the structural perturbation impact the global and local responses at different orders in time. We propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration.

cond-mat.dis-nn↗

arXiv2025

Including the magnitude variability of a signal into the ordinal pattern analysis

One of the most popular and innovative methods to analyse signals is by using Ordinal Patterns (OPs). The OP encoding is based on transforming a (univariate) signal into a symbolic sequence of OPs, where each OP represents the number of permutations needed to order a small subset of the signal's magnitudes. This implies that OPs are conceptually clear, methodologically simple to implement, robust to noise, and can be applied to short signals. Moreover, they simplify the statistical analyses that can be carried out on a signal, such as entropy and complexity quantifications. However, because of the relative ordering, information about the magnitude of the signal at each timestamp is lost -- this being one of the major drawbacks in the method. Here, we propose a way to use the signal magnitudes discarded in the OP encoding as a complementary variable to its permutation entropy. To illustrate our approach, we analyse synthetic trajectories from logistic and H{\'e}non maps -- with and without added noise -- and intracranial electroencephalographic recordings from rats in different sleep-wake states. Our results show that, when complementing the permutation entropy with the variability in the signal magnitudes, the characterisation of the dynamical behaviours of the maps and the sleep-wake states is improved. This implies that our approach can be useful for feature engineering and improving AI classifiers, where typical machine learning algorithms need complementary signal features as inputs to improve classification accuracy.

nlin.CD↗

arXiv2024

Nontrivial Kron Reduction for Power Grid Dynamics Modeling

The Kron reduction is used in power grid modeling when the analysis can -- supposedly -- be restricted to a subset of nodes. Typically, when one is interested in the phases' dynamics, it is common to reduce the load buses and focus on the generators' behavior. The rationale behind this reduction is that voltage phases at load buses adapt quickly to their neighbors' phases and, at the timescale of generators, they have virtually no dynamics. We show that the dynamics of the Kron-reduced part of a network can have a significant impact on the dynamics of the non-reduced buses. Therefore, Kron reduction should be used with care and, depending on the context, reduced nodes cannot be simply ignored. We demonstrate that the noise in the reduced part can unexpectedly affect the non-reduced part, even under the assumption that nodal disturbances are independent. Therefore, the common assumption that the noise in the non-reduced part is uncorrelated may lead to inaccurate assessments of the grid's behavior. To cope with such shortcomings of the Kron reduction, we show how to properly incorporate the contribution of the reduced buses into the reduced model using the Mori-Zwanzig formalism.

math.DS↗

arXiv2024

Forced oscillation source localization from generator measurements

Malfunctioning equipment, erroneous operating conditions or periodic load variations can cause periodic disturbances that would persist over time, creating an undesirable transfer of energy across the system -- an effect referred to as forced oscillations. Wide-area oscillations may damage assets, trigger inadvertent tripping or control actions, and be the cause of equipment failure. Unfortunately, for wide-area oscillations, the location, frequency, and amplitude of these forced oscillations may be hard to determine. Recently, a data-driven maximum-likelihood-based method was proposed to perform source localization in transmission grids under wide-area response scenarios. However, this method relies on full PMU coverage and all buses having inertia and damping. Here, we extend this method to realistic scenarios which includes buses without inertia or dumping, such as passive loads and inverter-based generators. Incorporating Kron reduction directly into the maximum likelihood estimator, we are able to identify the location and frequency of forcing applied at both traditional generators and loads.

eess.SY↗

arXiv2024

Resilience of the slow component in timescale separated synchronized oscillators

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently. Here, we focus on the case where synchronized oscillators are divided into a fast and a slow component so that the two subsets evolve on separated timescales. We assess the resilience of the slow component by reducing the dynamics of the fast one and evaluating the variance of the phase deviations when the oscillators in the two components are subject to noise with possibly distinct correlation times. From the general expression for the variance, we consider specific network structures and show how the noise transmission between the fast and slow components is affected. Interestingly, we find that oscillators that are among the most robust when there is only a single timescale, might become the most vulnerable when the system separates into two timescales. We also find that layered networks seem to be insensitive to timescale separations when the noise has homogeneous correlation time.

nlin.AO↗

arXiv2023

Assessing the impact of Byzantine attacks on coupled phase oscillators

For many coupled dynamical systems, the interaction is the outcome of the measurement that each unit has of the others as e.g. in modern inverter-based power grids, autonomous vehicular platoons or swarms of drones, or it is the results of physical flows. Synchronization among all the components of these systems is of primal importance to avoid failures. The overall operational state of these systems therefore crucially depends on the correct and reliable functioning of the individual elements as well as the information they transmit through the network. Here, we investigate the effect of Byzantine attacks where one unit does not behave as expected, but is controlled by an external attacker. For such attacks, we assess the impact on the global collective behavior of nonlinearly coupled phase oscillators. We relate the synchronization error induced by the input signal to the properties of the attacked node. This allows to anticipate the potential of an attacker and identify which network components to secure.

nlin.AO↗

arXiv2023

Evolution of robustness in growing random networks

Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of networks, this means that the number of nodes and edges change in time. Various properties of coupled dynamical systems essentially depend on the structure of the interaction network, such as their robustness to noise. It is therefore of interest to predict how these properties are affected when the network grows and what is their relation to the growing mechanism. Here, we focus on the time-evolution of the network's Kirchhoff index. We derive closed form expressions for its variation in various scenarios including both the addition of edges and nodes. For the latter case, we investigate the evolution where a single node with one and two edges connecting to existing nodes are added recursively to a network. In both cases we derive relations between the properties of the nodes to which the new one connects, and the global evolution of the network robustness. In particular, we show how different scalings of the Kirchhoff index as a function of the number of nodes are obtained. We illustrate and confirm the theory with numerical simulations of growing random networks.

nlin.AO↗

arXiv2023

Large and small fluctuations in oscillator networks from heterogeneous and correlated noise

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise. In this manuscript, we focus on the assessment of fluctuations resulting from heterogeneous and correlated noise inputs on Kuramoto model networks. We evaluate the typical, small fluctuations near synchronized states and connect the network variance to the overlap between stable modes of synchronization and the input noise covariance. Going beyond small to large fluctuations, we introduce the indicator mode approximation, that projects the dynamics onto a single amplitude dimension. Such an approximation allows for estimating rates of fluctuations to saddle instabilities, resulting in phase slips between connected oscillators. Statistics for both regimes are quantified in terms of effective noise amplitudes that are compared and contrasted for several noise models. Bridging the gap between small and large fluctuations, we show that a larger network variance does not necessarily lead to higher rates of large fluctuations.

nlin.PS↗

arXiv2023

Locating the source of forced oscillations in transmission power grids

Forced oscillation event in power grids refers to a state where malfunctioning or abnormally operating equipment causes persisting periodic disturbances in the system. While power grids are designed to damp most of perturbations during standard operations, some of them can excite normal modes of the system and cause significant energy transfers across the system, creating large oscillations thousands of miles away from the source. Localization of the source of such disturbances remains an outstanding challenge due to a limited knowledge of the system parameters outside of the zone of responsibility of system operators. Here, we propose a new method for locating the source of forced oscillations which addresses this challenge by performing a simultaneous dynamic model identification using a principled maximum likelihood approach. We illustrate the validity of the algorithm on a variety of examples where forcing leads to resonance conditions in the system dynamics. Our results establish that an accurate knowledge of system parameters is not required for a successful inference of the source and frequency of a forced oscillation. We anticipate that our method will find a broader application in general dynamical systems that can be well-described by their linearized dynamics over short periods of time.

nlin.AO↗

arXiv2023

Faster network disruption from layered oscillatory dynamics

Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium and, depending on the direction and the amplitude of the excursion, might undergo a transition to another equilibrium. It was recently demonstrated [M. Tyloo, J. Phys. Complex. 3 03LT01 (2022)], that layered complex networks may exhibit amplified fluctuations. Here I investigate how noise with system-specific correlations impacts the first escape time of nonlinearly coupled oscillators. Interestingly, I show that, not only the strong amplification of the fluctuations is a threat to the good functioning of the network, but also the spatial and temporal correlations of the noise along the lowest-lying eigenmodes of the Laplacian matrix. I analyze first escape times on synthetic networks and compare noise originating from layered dynamics, to uncorrelated noise.

nlin.AO↗

arXiv2022

Heavy-Tailed Distribution of the Number of Papers within Scientific Journals

Scholarly publications represent at least two benefits for the study of the scientific community as a social group. First, they attest of some form of relation between scientists (collaborations, mentoring, heritage,...), useful to determine and analyze social subgroups. Second, most of them are recorded in large data bases, easily accessible and including a lot of pertinent information, easing the quantitative and qualitative study of the scientific community. Understanding the underlying dynamics driving the creation of knowledge in general, and of scientific publication in particular can contribute to maintaining a high level of research, by identifying good and bad practices in science. In this article, we aim at advancing this understanding by a statistical analysis of publication within peer-reviewed journals. Namely, we show that the distribution of the number of papers published by an author in a given journal is heavy-tailed, but has lighter tail than a power law. Interestingly, we demonstrate (both analytically and numerically) that such distributions match the result of an modified preferential attachment process, where, on top of a Barabási-Albert process, we take finite career span of scientists into account.

cs.DL↗

arXiv2022

Layered Complex Networks as Fluctuation Amplifiers

In complex networked systems theory, an important question is how to evaluate the system robustness to external perturbations. With this task in mind, I investigate the propagation of noise in multi-layer networked systems. I find that, for a two layer network, noise originally injected in one layer can be strongly amplified in the other layer, depending on how well-connected are the complex networks in each layer and on how much the eigenmodes of their Laplacian matrices overlap. These results allow to predict potentially harmful conditions for the system and its sub-networks, where the level of fluctuations is important, and how to avoid them. The analytical results are illustrated numerically on various synthetic networks.

nlin.AO↗

arXiv2022

Locating fast-varying line disturbances with the frequency mismatch

In an attempt to provide an efficient method for line disturbance identification in complex networks of diffusively coupled agents, we recently proposed to leverage the frequency mismatch. The frequency mismatch filters out the intricate combination of interactions induced by the network structure and quantifies to what extent the trajectory of each agent is affected by the disturbance. In this previous work, we provided some analytical evidence of its efficiency when the perturbation is assumed to be slow. In the present work, we claim that the frequency mismatch performs actually well for most disturbance regimes. This is shown through a series of simulations and is backed up by an analytical argument. Therefore, we argue that the frequency mismatch is an efficient and elegant tool for line disturbance location in complex networks of diffusively coupled agents.

nlin.AO↗