arXiv subjects

Chiara Cicolani

Publications and source records attributed to Chiara Cicolani.

7 recordsLinked to original sources

arXiv2026

Asymptotic consensus and flocking under decaying persistent excitation on rooted digraphs

In this paper, we investigate first- and second-order alignment models with non-universal interaction, time delays and possible communication failures, extending the results in [17] to interaction digraphs that are only assumed to be rooted and to a weaker Persistence Excitation Condition. In particular, we allow the amount of interaction over time intervals of fixed length to decay polynomially in time. For the first-order Hegselmann-Krause type model, we prove asymptotic convergence to consensus under a suitable condition relating the decay exponent of the communication weights to the maximal distance from the root. For the second-order Cucker-Smale model, we establish asymptotic flocking under an additional assumption on the decay of the influence function. These results show that collective behavior can still emerge under progressively weakening communication and without requiring strong connectivity of the interaction graph.

math.OC↗

arXiv2026

Flocking and Mean-Field Analysis of Delayed Leader-Follower Cucker-Smale System

Inspired by \cite{CCP}, we investigate a delayed leader-follower Cucker-Smale model describing the collective dynamics of interacting agents subject to communication lags. We first study the particle dynamics and establish sufficient conditions ensuring the emergence of asymptotic flocking. Our analysis shows that velocity alignment and bounded spatial dispersion persist despite the presence of delays and heterogeneous interactions between leaders and followers. We then derive and analyze two continuum descriptions of the system. In the first regime, the number of leaders is kept fixed while the number of followers tends to infinity, leading to a hybrid particle-kinetic model. In the second regime, both populations become infinitely large, yielding a fully kinetic delayed leader-follower model. For both mean-field formulations, we prove global existence, uniqueness, and Wasserstein stability of measure-valued solutions. These results provide a rigorous mathematical framework for the study of collective dynamics with leadership and memory effects and establish a bridge between delayed flocking models and their continuum counterparts.

math.AP↗

arXiv2025

Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits

We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the same time, non-leaders update their opinions via interactions with their peers and the leaders, with time delays accounting for communication and decision-making lags. We prove the exponential convergence to consensus of the particle system, without imposing smallness assumptions on the delay parameters. Furthermore, we analyze the mean-field limit in two regimes: (i) with a fixed number of leaders and an infinite number of non-leaders, and (ii) with both populations tending to infinity, obtaining existence, uniqueness, and exponential decay estimates for the corresponding macroscopic models.

math.AP↗

arXiv2024

Opinion dynamics under common influencer assumption or leadership control

We study Hegselmann-Krause type opinion formation models with non-universal interaction and time-delayed coupling. We assume the presence of a common influencer between two different agents. Moreover, we explore two cases in which such an assumption does not hold but leaders with independent opinion are present. By using careful estimates on the system's trajectories, we are able to prove asymptotic convergence to consensus estimates. Some numerical tests illustrate the theoretical results.

math.OC↗

arXiv2024

First and second-order Cucker-Smale models with non-universal interaction, time delay and communication failures

In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not transmit information to all the other agents and also agents that are linked to each other can suspend their interaction at certain times. Moreover, we take into account of possible time lags in the interactions. To deal with the considered "non-universal" connection, a graph topology over the structure of the model has to be considered. Under a so-called Persistence Excitation Condition, we establish the exponential convergence to consensus for both models whenever the digraph that describes the interaction between the agents is strongly connected.

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arXiv2024

Asymptotic synchronization of Kuramoto oscillators with time delay and non-universal interaction

We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the asymptotic frequency synchronization of the oscillators under suitable assumptions on the initial configurations. In the case of an all-to-all connection, we obtain an exponential synchronization estimate. Additionally, we present numerical simulations, providing further insights into the synchronization and oscillatory behaviors of the oscillator frequencies depending on the network structure and the magnitude of the time delay.

math.OC↗

arXiv2024

Opinion dynamics of two populations with time-delayed coupling

We study a Hegselmann-Krause type opinion formation model for a system of two populations. The two groups interact with each other via subsets of individuals, namely the leaders, and natural time delay effects are considered. By using careful estimates of the system's trajectories, we are able to prove an asymptotic convergence to consensus result. Some numerical tests illustrate the theoretical result and point out some possible applications.

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