arXiv subjects

Mengbin Ye

Publications and source records attributed to Mengbin Ye.

At least 37 records · Page 2Linked to original sources

arXiv2023

On Adaptive-Gain Control of Replicator Dynamics in Population Games

Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals who play a generic 2-action matrix game, and whose actions evolve according to a replicator equation -- a nonlinear ordinary differential equation that captures salient features of the collective behavior of the population. Our objective is to steer such a population to a specified equilibrium that represents a desired collective behavior -- e.g., to promote cooperation in the prisoner's dilemma. To this aim, we devise an adaptive-gain controller, which regulates the system dynamics by adaptively changing the entries of the payoff matrix of the game. The adaptive-gain controller is tailored according to distinctive features of the game, and conditions to guarantee global convergence to the desired equilibrium are established.

eess.SY↗

arXiv2023

Coevolutionary Dynamics of Actions and Opinions in Social Networks

Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap in the literature by proposing a novel coevolutionary model, in which each individual selects an action from a binary set and has an opinion on which action they prefer. Actions and opinions coevolve on a two-layer network. For homogeneous parameters, undirected networks, and under reasonable assumptions on the asynchronous updating mechanics, we prove that the coevolutionary dynamics is an ordinal potential game, enabling analysis via potential game theory. Specifically, we establish global convergence to the Nash equilibria of the game, proving that actions converge in a finite number of time steps, while opinions converge asymptotically. Next, we provide sufficient conditions for the existence of, and convergence to, polarized equilibria, whereby the population splits into two communities, each selecting and supporting one of the actions. Finally, we use simulations to examine the social psychological phenomenon of pluralistic ignorance.

eess.SY↗

arXiv2023

Equilibria analysis of a networked bivirus epidemic model using Poincaré--Hopf and Manifold Theory

This paper considers a deterministic Susceptible-Infected-Susceptible (SIS) networked bivirus epidemic model (termed the bivirus model for short), in which two competing viruses spread through a set of populations (nodes) connected by two graphs, which may be different if the two viruses have different transmission pathways. The networked dynamics can give rise to complex equilibria patterns, and most current results identify conditions on the model parameters for convergence to the healthy equilibrium (where both viruses are extinct) or a boundary equilibrium (where one virus is endemic and the other is extinct). However, there are only limited results on coexistence equilibria (where both viruses are endemic). This paper establishes a set of ``counting'' results which provide lower bounds on the number of coexistence equilibria, and perhaps more importantly, establish properties on the local stability/instability properties of these equilibria. In order to do this, we employ the Poincaré-Hopf Theorem but with significant modifications to overcome several challenges arising from the bivirus system model, such as the fact that the system dynamics do not evolve on a manifold in the typical sense required to apply Poincaré-Hopf Theory. Subsequently, Morse inequalities are used to tighten the counting results, under the reasonable assumption that the bivirus system is a Morse-Smale dynamical system. Numerical examples are provided which demonstrate the presence of multiple attractor equilibria, and multiple coexistence equilibria.

math.DS↗

arXiv2023

Decentralised adaptive-gain control for eliminating epidemic spreading on networks

This paper considers the classical Susceptible--Infected--Susceptible (SIS) network epidemic model, which describes a disease spreading through $n$ nodes, with the network links governing the possible transmission pathways of the disease between nodes. We consider feedback control to eliminate the disease in scenarios where the disease would otherwise persist in an uncontrolled network. We propose a family of decentralised adaptive-gain control algorithms, in which each node has a control gain that adaptively evolves according to a differential equation, independent of the gains of other nodes. The adaptive gain is applied multiplicatively to either decrease the infection rate or increase the recovery rate. To begin, we assume all nodes are controlled, and prove that both infection rate control and recovery rate control algorithms eliminate the disease with the limiting gains being positive and finite. Then, we consider the possibility of controlling a subset of the nodes, for both the infection rate control and recovery rate control. We first identify a necessary and sufficient condition for the existence of a subset of nodes, which if controlled would result in the elimination of the disease. For a given network, there may exist several such viable subsets, and we propose an iterative algorithm to identify such a subset. Simulations are provided to demonstrate the effectiveness of the various proposed controllers.

eess.SY↗

arXiv2023

Towards Understanding the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model

This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. Specifically, the paper deals with three competing virus systems (i.e., tri-virus systems). First, we show that a tri-virus system, unlike a bi-virus system, is not a monotone dynamical system. Using the Parametric Transversality Theorem, we show that, generically, a tri-virus system has a finite number of equilibria and that the Jacobian matrices associated with each equilibrium are nonsingular. The endemic equilibria of this system can be classified as follows: a) single-virus endemic equilibria (also referred to as the boundary equilibria), where precisely one of the three viruses is alive; b) 2-coexistence equilibria, where exactly two of the three viruses are alive; and c) 3-coexistence equilibria, where all three viruses survive in the network. We provide a necessary and sufficient condition that guarantees local exponential convergence to a boundary equilibrium. Further, we secure conditions for the nonexistence of 3-coexistence equilibria (resp. for various forms of 2-coexistence equilibria). We also identify sufficient conditions for the existence of a 2-coexistence (resp. 3-coexistence) equilibrium. We identify conditions on the model parameters that give rise to a continuum of coexistence equilibria. More specifically, we establish i) a scenario that admits the existence and local exponential attractivity of a line of coexistence equilibria; and ii) scenarios that admit the existence of, and, in the case of one such scenario, global convergence to, a plane of 3-coexistence equilibria.

eess.SY↗

arXiv2023

Competitive epidemic networks with multiple survival-of-the-fittest outcomes

We use a deterministic model to study two competing viruses spreading over a two-layer network in the Susceptible--Infected--Susceptible (SIS) framework, and address a central problem of identifying the winning virus in a "survival-of-the-fittest" battle. Existing sufficient conditions ensure that the same virus always wins regardless of initial states. For networks with an arbitrary but finite number of nodes, there exists a necessary and sufficient condition that guarantees local exponential stability of the two equilibria corresponding to each virus winning the battle, meaning that either of the viruses can win, depending on the initial states. However, establishing existence and finding examples of networks with more than three nodes that satisfy such a condition has remained unaddressed. In this paper, we prove that, for any arbitrary number of nodes, such networks exist. We do this by proving that given almost any network layer of one virus, there exists a network layer for the other virus such that the resulting two-layer network satisfies the aforementioned condition. To operationalize our findings, a four-step procedure is developed to reliably and consistently design one of the network layers, when given the other layer. Conclusions from numerical case studies, including a real-world mobility network that captures the commuting patterns for people between $107$ provinces in Italy, extend on the theoretical result and its consequences.

math.DS↗

arXiv2022

On the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model

This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. In particular, we focus on the case where there are three competing viruses (i.e., the tri-virus system). First, we show that the tri-virus system is not a monotone system. Thereafter, we provide a condition that guarantees local exponential convergence to a boundary equilibrium (exactly one virus is endemic, the other two are dead), and identify a special case that admits the existence and local exponential attractivity of a line of coexistence equilibria (at least two viruses are active). Finally, we identify a particular case (subsumed by the aforementioned special case) such that, for all nonzero initial infection levels, the dynamics of the tri-virus system converge to a plane of coexistence equilibria.

eess.SY↗

arXiv2022

Demystifying the COVID-19 vaccine discourse on Twitter

Developing an understanding of the public discourse on COVID-19 vaccination on social media is important not only for addressing the current COVID-19 pandemic, but also for future pathogen outbreaks. We examine a Twitter dataset containing 75 million English tweets discussing COVID-19 vaccination from March 2020 to March 2021. We train a stance detection algorithm using natural language processing (NLP) techniques to classify tweets as `anti-vax' or `pro-vax', and examine the main topics of discourse using topic modelling techniques. While pro-vax tweets (37 million) far outnumbered anti-vax tweets (10 million), a majority of tweets from both stances (63% anti-vax and 53% pro-vax tweets) came from dual-stance users who posted both pro- and anti-vax tweets during the observation period. Pro-vax tweets focused mostly on vaccine development, while anti-vax tweets covered a wide range of topics, some of which included genuine concerns, though there was a large dose of falsehoods. A number of topics were common to both stances, though pro- and anti-vax tweets discussed them from opposite viewpoints. Memes and jokes were amongst the most retweeted messages. Whereas concerns about polarisation and online prevalence of anti-vax discourse are unfounded, targeted countering of falsehoods is important.

cs.SI↗

arXiv2022

A mean-field analysis of a network behavioural-epidemic model

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioural-epidemic model, in which a susceptible-infected-susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterise the asymptotic behaviour of the system, deriving conditions for global convergence to a disease-free equilibrium and characterising the endemic equilibria of the system and their (local) stability. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterised by periodic epidemic outbreaks.

math.DS↗

arXiv2021

Convergence and Equilibria Analysis of a Networked Bivirus Epidemic Model

This paper studies a networked bivirus model, in which two competing viruses spread across a network of interconnected populations; each node represents a population with a large number of individuals. The viruses may spread through possibly different network structures, and an individual cannot be simultaneously infected with both viruses. Focusing on convergence and equilibria analysis, a number of new results are provided. First, we show that for networks with generic system parameters, there exist a finite number of equilibria. Exploiting monotone systems theory, we further prove that for bivirus networks with generic system parameters, then convergence to an equilibrium occurs for all initial conditions, except possibly for a set of measure zero. Given the network structure of one virus, a method is presented to construct an infinite family of network structures for the other virus that results in an infinite number of equilibria in which both viruses coexist. Necessary and sufficient conditions are derived for the local stability/instability of boundary equilibria, in which one virus is present and the other is extinct. A sufficient condition for a boundary equilibrium to be almost globally stable is presented. Then, we show how to use monotone systems theory to generate conclusions on the ordering of stable and unstable equilibria, and in some instances identify the number of equilibria via rapid simulation testing. Last, we provide an analytical method for computing equilibria in networks with only two nodes, and show that it is possible for a bivirus network to have an unstable coexistence equilibrium and two locally stable boundary equilibria.

math.DS↗

arXiv2021

Game-theoretic modeling of collective decision-making during epidemics

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral--epidemic model, in which an interplay of realistic factors shapes the co-evolution of individual decision-making and epidemics on a network. Although such a co-evolution is deeply intertwined in the real-world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our model offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.

q-bio.PE↗

arXiv2021

A two-layer model for coevolving opinion dynamics and collective decision-making in complex social systems

Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others' opinions shared on a communication channel, and observe of others' actions through an influence channel; these interactions determine a two-layer network structure. We offer an application of the proposed framework by tailoring it to study the adoption of a novel social norm, demonstrating that the model is able to capture the emergence of several real-world collective phenomena such as paradigm shifts and unpopular norms. Through the establishment of analytical conditions and Monte Carlo numerical simulations, we shed light on the role of the coupling between opinion dynamics and decision-making, and of the network structure, in shaping the emergence of complex collective behavior in social systems.

cs.SI↗

arXiv2020

Applications of the Poincaré--Hopf Theorem: Epidemic Models and Lotka--Volterra Systems

This paper focuses on the equilibria and their regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincaré--Hopf Theorem from differential topology is used to derive a result on a sufficient condition on the Jacobian for the existence of a unique equilibrium for the system, which is in fact locally exponentially stable. We show how to apply this result to the deterministic SIS networked model, and a nonlinear Lotka--Volterra system. We apply the result further to establish an impossibility conclusion for a class of distributed feedback controllers whose goal is to drive the SIS network to the zero equilibrium. Specifically, we show that if the uncontrolled system has a unique nonzero equilibrium (a diseased steady-state), then the controlled system also has a unique nonzero equilibrium. Applying results from monotone dynamical systems theory, we further show that both the uncontrolled and controlled system will converge to their nonzero equilibrium from all nonzero initial conditions exponentially fast. A counterpart sufficient condition for the existence of a unique equilibrium for a nonlinear discrete-time dynamical system is also presented.

math.DS↗

arXiv2020

Forced variational integrator for distance-based shape control with flocking behavior of multi-agent systems

A multi-agent system designed to achieve distance-based shape control with flocking behavior can be seen as a mechanical system described by a Lagrangian function and subject to additional external forces. Forced variational integrators are given by the discretization of Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. We derive forced variational integrators that can be employed in the context of control algorithms for distance-based shape with velocity consensus. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions, while preserving the configuration space and symmetries. We also provide an explicit expression for the integration scheme in the case of an arbitrary number of agents with double integrator dynamics. For a numerical comparison of the performances, we use a planar formation consisting of three autonomous agents.

eess.SY↗

arXiv2020

Analysis of a Nonlinear Opinion Dynamics Model with Biased Assimilation

This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude of this parameter reflects an individual's degree of bias when assimilating new opinions, and depending on the magnitude, an individual is said to have weak, intermediate, and strong bias. The opinions of the individuals lie between 0 and 1. It is shown that for strongly connected networks, the equilibria with all elements equal identically to the extreme value 0 or 1 is locally exponentially stable, while the equilibrium with all elements equal to the neutral consensus value of 1/2 is unstable. Regions of attraction for the extreme consensus equilibria are given. For the equilibrium consisting of both extreme values 0 and 1, which corresponds to opinion polarization according to the model, it is shown that the equilibrium is unstable for all strongly connected networks if individuals all have weak bias, becomes locally exponentially stable for complete and two-island networks if individuals all have strong bias, and its stability heavily depends on the network topology when individuals have intermediate bias. Analysis on star graphs and simulations show that additional equilibria may exist where individuals form clusters.

math.OC↗

arXiv2020

Continuous-time Opinion Dynamics on Multiple Interdependent Topics

In this paper, and inspired by the recent discrete-time model in [1,2], we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a `logic' matrix, which is distinct from the Laplacian matrix capturing interactions between individuals. For each of Model 1 and Model 2, we obtain a necessary and sufficient condition for the network to reach to a consensus on each separate topic. The condition on Model 1 involves a combination of the eigenvalues of the logic matrix and Laplacian matrix, whereas the condition on Model 2 requires only separate conditions on the logic matrix and Laplacian matrix. Further investigations of Model 1 yields two sufficient conditions for consensus, and allow us to conclude that one way to guarantee a consensus is to reduce the rate of interaction between individuals exchanging opinions. By placing further restrictions on the logic matrix, we also establish a set of Laplacian matrices which guarantee consensus for Model 1. The two models are also expanded to include stubborn individuals, who remain attached to their initial opinions. Sufficient conditions are obtained for guaranteeing convergence of the opinion dynamics system, with the final opinions generally being at a persistent disagreement. Simulations are provided to illustrate the results.

cs.SI↗

arXiv2019

An Influence Network Model to Study Discrepancies in Expressed and Private Opinions

In many social situations, a discrepancy arises between an individual's private and expressed opinions on a given topic. Motivated by Solomon Asch's seminal experiments on social conformity and other related socio-psychological works, we propose a novel opinion dynamics model to study how such a discrepancy can arise in general social networks of interpersonal influence. Each individual in the network has both a private and an expressed opinion: an individual's private opinion evolves under social influence from the expressed opinions of the individual's neighbours, while the individual determines his or her expressed opinion under a pressure to conform to the average expressed opinion of his or her neighbours, termed the local public opinion. General conditions on the network that guarantee exponentially fast convergence of the opinions to a limit are obtained. Further analysis of the limit yields several semi-quantitative conclusions, which have insightful social interpretations, including the establishing of conditions that ensure every individual in the network has such a discrepancy. Last, we show the generality and validity of the model by using it to explain and predict the results of Solomon Asch's seminal experiments.

cs.SI↗

arXiv2019

Cooperative opinion dynamics on multiple interdependent topics: Modeling and analysis

To model the interdependent couplings of multiple topics, we develop a set of rules for opinion updates of a group of agents. The rules are used to design or assign values to the elements of interdependent weighting matrices. The cooperative and anti-cooperative couplings are modeled in both the inverse-proportional and proportional feedbacks. The behaviors of cooperative opinion dynamics are analyzed using a null space property of state-dependent matrix-weighted Laplacian matrices and a Lyapunov candidate. Various consensus properties of state-dependent matrix-weighted Laplacian matrices are predicted according to the intra-agent network topology and inter-dependency topical coupling topologies.

eess.SY↗