arXiv subjects

Juan G. Restrepo

Publications and source records attributed to Juan G. Restrepo.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics tuning with reservoir computer control

We present an equation-free method for maintaining a dynamical system operating in a desired regime, even as system parameters are disturbed in such a way that qualitatively different dynamics would emerge. This method allows for real-time identification of changes made to a system's evolution equations induced by the parameter changes. If the equations governing the original system's dynamics are known, our method can allow one to determine the values of the parameters in real time. We illustrate our method with numerical examples using a reservoir computer control implementation.

nlin.CD↗

arXiv2026

Low-dimensional Dynamics of the Social Compass Model

The social compass model has been recently proposed as a model for depolarization in populations where individuals have multiple, possibly correlated, opinions. Previous work has focused on the steady state of this model, but has not addressed the dynamics leading to depolarization. We show that the macroscopic dynamics of the social compass model can be described using the Ott-Antonsen Ansatz and that, for initially clustered opinions, the resulting equations reduce to a finite-dimensional system of ordinary differential equations. We study the linear stability of the polarized state and find a dispersion relation for the growth rate of perturbations from this state. We find that the critical coupling for depolarization depends only on the first inverse moment of the conviction distribution, whereas the rate of depolarization depends on higher moments. Consequently, conviction distributions with the same critical coupling can exhibit vastly different depolarization timescales. We also demonstrate how our analysis can be extended to study depolarization in the presence of community structure.

physics.soc-ph↗

arXiv2026

Self-consistent analysis of the Kuramoto model with higher-order interactions

The Kuramoto model with higher-order interactions has recently been shown to exhibit bistability, explosive synchronization transitions, and rich collective dynamics. Existing analytical approaches, however, typically rely on all-to-all coupling or mean-field approximations of the underlying hypergraph structure. While these methods describe typical networks in the thermodynamic limit, they generally fail to capture the effects of finite hypergraph and oscillator frequency realizations. To address this limitation, we develop a self-consistent analytical framework for the Kuramoto model with dyadic and triadic interactions on hypergraphs. We introduce generalized local order parameters that capture the combined effects of dyadic and triadic phase correlations, and derive a hierarchy of approximation schemes for the local and global synchronization order parameters. Using these approximations, we determine critical coupling strengths for the onset of synchronization and bistability. In particular, we show that the critical triadic coupling strength governing the onset of bistability depends on correlations between the eigenvectors of the dyadic adjacency matrix and the triadic interaction structure. Numerical simulations on homogeneous and heterogeneous hypergraphs validate the theory and illustrate the distinct regimes of applicability of the approximation schemes.

nlin.AO↗

arXiv2026

A Utility-Driven Bounded-Confidence Model for Opinion Dynamics

We introduce a utility-driven bounded-confidence model of opinion dynamics in which opinions associated with higher utility exert stronger social influence. In the regime where all agents belong to a single opinion cluster, we derive a stochastic differential equation for the mean opinion and show that its stationary distribution is Gibbs-like, with an effective potential determined by the utility landscape and an inverse temperature controlled by the learning rate and the number of agents. For multimodal utility functions, the dynamics exhibit metastability and spontaneous switching between competing opinion states. The reduced stochastic description also captures the evolution and merging of multiple opinion clusters, in agreement with agent-based simulations.

nlin.AO↗

arXiv2025

Macroscopic dynamics of oscillator ensembles with communities, higher-order interactions, and phase lags

We study the effects of phase-frustrated, higher-order interactions in a system of coupled phase oscillators with two communities. We use dimensionality reduction techniques to derive a low-dimensional system of ODEs to describe the macroscopic behavior of the system. By analyzing this system we show that, in addition to the fixed point solutions present in a system of oscillators with higher order interactions and community structure only, the system also exhibits oscillatory or chaotic synchronization behavior for some phase lag values. Moreover, some phase lag values give rise to multistability of solutions, where both fixed point solutions and oscillatory or chaotic behavior of the order parameters can be observed, depending on initial conditions.

nlin.AO↗

arXiv2025

Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions

In traditional models of opinion dynamics, each agent in a network has an opinion and changes in opinions arise from pairwise (i.e., dyadic) interactions between agents. However, in many situations, groups of individuals possess a collective opinion that can differ from the opinions of its constituent individuals. In this paper, we study the effects of group opinions on opinion dynamics. We formulate a hypergraph model in which both individual agents and groups of 3 agents have opinions, and we examine how opinions evolve through both dyadic interactions and group memberships. In some parameter regimes, we find that the presence of group opinions can lead to oscillatory and excitable opinion dynamics. In the oscillatory regime, the mean opinion of the agents in a network has self-sustained oscillations. In the excitable regime, finite-size effects create large but short-lived opinion swings (as in social fads). We develop a mean-field approximation of our model and obtain good agreement with direct numerical simulations. We also show -- both numerically and via our mean-field description -- that oscillatory dynamics occur only when the number of dyadic and polyadic interactions per agent are not completely correlated. Our results illustrate how polyadic structures, such as groups of agents, can have important effects on collective opinion dynamics.

physics.soc-ph↗

arXiv2025

Competing Social Contagions with Opinion Dependent Infectivity

The spread of disinformation (maliciously spread false information) in online social networks has become an important problem in today's society. Disinformation's spread is facilitated by the fact that individuals often accept false information based on cognitive biases which predispose them to believe information that they have heard repeatedly or that aligns with their beliefs. Moreover, disinformation often spreads in direct competition with a corresponding true information. To model these phenomena, we develop a model for two competing beliefs spreading on a social network, where individuals have an internal opinion that models their cognitive biases and modulates their likelihood of adopting one of the competing beliefs. By numerical simulations of an agent-based model and a mean-field description of the dynamics, we study how the long-term dynamics of the spreading process depends on the initial conditions for the number of spreaders and the initial opinion of the population. We find that the addition of cognitive biases enriches the transient dynamics of the spreading process, facilitating behavior such as the revival of a dying belief and the overturning of an initially widespread opinion. Finally, we study how external recruitment of spreaders can lead to the eventual dominance of one of the two beliefs.

physics.soc-ph↗

arXiv2024

Suppressing unknown disturbances to dynamical systems using machine learning

Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. Here we present a model-free method to identify and suppress an unknown disturbance to an unknown system based only on previous observations of the system under the influence of a known forcing function. We find that, under very mild restrictions on the training function, our method is able to robustly identify and suppress a large class of unknown disturbances. We illustrate our scheme with the identification of both deterministic and stochastic unknown disturbances to an analog electric chaotic circuit and with numerical examples where a chaotic disturbance to various chaotic dynamical systems is identified and suppressed.

eess.SY↗

arXiv2024

A theoretical framework for reservoir computing on networks of organic electrochemical transistors

Efficient and accurate prediction of physical systems is important even when the rules of those systems cannot be easily learned. Reservoir computing, a type of recurrent neural network with fixed nonlinear units, is one such prediction method and is valued for its ease of training. Organic electrochemical transistors (OECTs) are physical devices with nonlinear transient properties that can be used as the nonlinear units of a reservoir computer. We present a theoretical framework for simulating reservoir computers using OECTs as the non-linear units as a test bed for designing physical reservoir computers. We present a proof of concept demonstrating that such an implementation can accurately predict the Lorenz attractor with comparable performance to standard reservoir computer implementations. We explore the effect of operating parameters and find that the prediction performance strongly depends on the pinch-off voltage of the OECTs.

cs.NE↗

arXiv2024

Explicit solutions of the Bass and SI models on hypernetworks

We analyze the Bass model and the Susceptible-Infected (SI) model on hypergraphs with 3-body interactions. We derive the master equations for general hypernetworks, and use them to obtain explicit expressions for the expected adoption/infection level on infinite complete hypernetworks, infinite Erdős-Rényi hypernetworks, and on infinite hyperlines. These expressions are exact, as they are derived without making any approximation.

physics.soc-ph↗

arXiv2024

A dynamical system model of gentrification: Exploring a simple rent control strategy

Motivated by the need to understand the factors driving gentrification, we introduce and analyze two simple dynamical systems that model the interplay between three potential drivers of the phenomenon. The constructed systems are based on the assumption that three canonical drivers exist: a subpopulation that increases the desirability of a neighborhood, the desirability of a neighborhood, and the average price of real estate in a neighborhood. The second model modifies the first and implements a simple rent control scheme. For both models, we investigate the linear stability of equilibria and numerically determine the characteristics of oscillatory solutions as a function of system parameters. Introducing a rent control scheme stabilizes the system, in the sense that the parameter regime under which solutions approach equilibrium is expanded. However, oscillatory time series generated by the rent control model are generally more disorganized than those generated by the non-rent control model; in fact, long-term transient chaos was observed under certain conditions in the rent control case. Our results illustrate that even simple models of urban gentrification can lead to complex temporal behavior.

nlin.AO↗

arXiv2023

Tuning the activation function to optimize the forecast horizon of a reservoir computer

Reservoir computing is a machine learning framework where the readouts from a nonlinear system (the reservoir) are trained so that the output from the reservoir, when forced with an input signal, reproduces a desired output signal. A common implementation of reservoir computers is to use a recurrent neural network as the reservoir. The design of this network can have significant effects on the performance of the reservoir computer. In this paper we study the effect of the node activation function on the ability of reservoir computers to learn and predict chaotic time series. We find that the Forecast Horizon (FH), the time during which the reservoir's predictions remain accurate, can vary by an order of magnitude across a set of 16 activation functions used in machine learning. By using different functions from this set, and by modifying their parameters, we explore whether the entropy of node activation levels or the curvature of the activation functions determine the predictive ability of the reservoirs. We find that the FH is low when the activation function is used in a region where it has low curvature, and a positive correlation between curvature and FH. For the activation functions studied we find that the largest FH generally occurs at intermediate levels of the entropy of node activation levels. Our results show that the performance of reservoir computers is very sensitive to the activation function shape. Therefore, modifying this shape in hyperparameter optimization algorithms can lead to improvements in reservoir computer performance.

cs.NE↗

arXiv2023

Opinion disparity in hypergraphs with community structure

The division of a social group into subgroups with opposing opinions, which we refer to as opinion disparity, is a prevalent phenomenon in society. This phenomenon has been modeled by including mechanisms such as opinion homophily, bounded confidence interactions, and social reinforcement mechanisms. In this paper we study a complementary mechanism for the formation of opinion disparity based on higher-order interactions, i.e., simultaneous interactions between multiple agents. We present an extension of the planted partition model for uniform hypergraphs as a simple model of community structure and consider the hypergraph SIS model on a hypergraph with two communities where the binary ideology can spread via links (pairwise interactions) and triangles (three-way interactions). We approximate this contagion process with a mean-field model and find that for strong enough community structure, the two communities can hold very different average opinions. We determine the regimes of structural and infectious parameters for which this opinion disparity can exist and find that the existence of these disparities is much more sensitive to the triangle community structure than to the link community structure. We show that the existence and type of opinion disparities are extremely sensitive to differences in the sizes of the two communities.

physics.soc-ph↗

arXiv2023

Detecting disturbances in network-coupled dynamical systems with machine learning

Identifying disturbances in network-coupled dynamical systems without knowledge of the disturbances or underlying dynamics is a problem with a wide range of applications. For example, one might want to know which nodes in the network are being disturbed and identify the type of disturbance. Here we present a model-free method based on machine learning to identify such unknown disturbances based only on prior observations of the system when forced by a known training function. We find that this method is able to identify the locations and properties of many different types of unknown disturbances using a variety of known forcing functions. We illustrate our results both with linear and nonlinear disturbances using food web and neuronal activity models. Finally, we discuss how to scale our method to large networks.

cs.LG↗

arXiv2023

The Impact of Meta-Strategy on Attendance Dynamics in the El Farol Bar Problem

The El Farol Bar Problem is a classic computational economics problem in which agents attempt to attend a weekly event at a bar only if it is not too crowded. Each agent has access to multiple competing strategies that may be used to predict whether attendance will be above the tolerance threshold. Many different variations of the El Farol Bar Problem have been published, with a particularly broad variation in the choice of meta-strategy, the algorithm by which each agent selects the best-performing strategy. This paper discusses the varying mechanisms of self-organization within the system when different meta-strategies are used, including the existence and location of fixed points in the limit of an infinite number of agents. Informed by these mechanisms, we present an evolutionary paradigm that reduces the likelihood of degenerate cases where attendance is always too high or too low, while reducing the amplitude of fluctuations in attendance. This evolutionary paradigm sheds light on the critical role of heterogeneity of strategies selected in the emergence of a stable steady state in the El Farol Bar Problem.

nlin.AO↗

arXiv2023

Synchronization of phase oscillators on complex hypergraphs

We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of differential equations for the system's order parameters. We illustrate our framework with the example of a hypergraph with hyperedges of sizes 2 (links) and 3 (triangles). For this case, we obtain a set of 2 coupled nonlinear algebraic equations for the order parameters. For strong values of coupling via triangles, the system exhibits bistability and explosive synchronization transitions. We find conditions that lead to bistability in terms of hypergraph properties and validate our predictions with numerical simulations. Our results provide a general framework to study synchronization of phase oscillators in hypergraphs, and they can be extended to hypergraphs with hyperedges of arbitrary sizes, dynamic-structural correlations, and other features.

nlin.AO↗

arXiv2022

Multistability in coupled oscillator systems with higher-order interactions and community structure

We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by either higher-order interactions or community structure alone, including synchronized states with communities organized into clusters in-phase, anti-phase, and a novel skew-phase, as well as an incoherent-synchronized state. Moreover, the system displays a strong multistability, with many of these states stable at the same time. We demonstrate our findings by deriving the low dimensional dynamics of the system and examining the system's bifurcations using a stability analysis and perturbation theory.

nlin.AO↗

arXiv2022

Dirac synchronization is rhythmic and explosive

Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied in network dynamics, while topological signals defined on links are much less explored. Here we investigate Dirac synchronization, describing locally coupled topological signals defined on the nodes and on the links of a network, and treated using the topological Dirac operator. The dynamics of signals defined on the nodes is affected by a phase lag depending on the dynamical state of nearby links and vice versa. We show that Dirac synchronization on a fully connected network is explosive with a hysteresis loop characterized by a discontinuous forward transition and a continuous backward transition. The analytical investigation of the phase diagram provides a theoretical understanding of this topological explosive synchronization. The model also displays an exotic coherent synchronized phase, also called rhythmic phase, characterized by non-stationary order parameters which can shed light on topological mechanisms for the emergence of brain rhythms.

cond-mat.dis-nn↗