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Register a new userCooperative opinion dynamics on multiple interdependent topics: Modeling and analysis
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Added by
Hyo-Sung Ahn
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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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.
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We propose a mathematical model to study coupled epidemic and opinion dynamics in a network of communities. Our model captures SIS epidemic dynamics whose evolution is dependent on the opinions of the communities toward the epidemic, and vice versa. In particular, we allow both cooperative and antagonistic interactions, representing similar and opposing perspectives on the severity of the epidemic, respectively. We propose an Opinion-Dependent Reproduction Number to characterize the mutual influence between epidemic spreading and opinion dissemination over the networks. Through stability analysis of the equilibria, we explore the impact of opinions on both epidemic outbreak and eradication, characterized by bounds on the Opinion-Dependent Reproduction Number. We also show how to eradicate epidemics by reshaping the opinions, offering researchers an approach for designing control strategies to reach target audiences to ensure effective epidemic suppression.
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In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We examine asynchronous networks that are subject to fairly general sources of uncertainties, such as changing topologies, random link failures, random data arrival times, and agents turning on and off randomly. Under this model, agents in the network may stop updating their solutions or may stop sending or receiving information in a random manner and without coordination with other agents. We establish in Part I conditions on the first and second-order moments of the relevant parameter distributions to ensure mean-square stable behavior. We derive in Part II expressions that reveal how the various parameters of the asynchronous behavior influence network performance. We compare in Part III the performance of asynchronous networks to the performance of both centralized solutions and synchronous networks. One notable conclusion is that the mean-square-error performance of asynchronous networks shows a degradation only of the order of $O( u)$, where $ u$ is a small step-size parameter, while the convergence rate remains largely unaltered. The results provide a solid justification for the remarkable resilience of cooperative networks in the face of random failures at multiple levels: agents, links, data arrivals, and topology.
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