### Citations

289 |
Statistical physics of social dynamics
- Castellano, Fortunato, et al.
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Citation Context ... of researchers in different areas including social science, economics, statistical physics, and systems and control [1], [4], [9], [10], [18], [16]. A comprehensive survey up to 2009 is available in =-=[5]-=-. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of others which are within a confidence interval. A slightly different rule was propose... |

228 | Opinion dynamics and bounded confidence models, analysis, and simulation
- Hegselmann, Krause
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Citation Context ...ies on social opinion formation have attracted considerable interest of researchers in different areas including social science, economics, statistical physics, and systems and control [1], [4], [9], =-=[10]-=-, [18], [16]. A comprehensive survey up to 2009 is available in [5]. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of others which are ... |

159 |
Mixing beliefs among interacting agents
- Deffuant, Neau, et al.
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Citation Context ... studies on social opinion formation have attracted considerable interest of researchers in different areas including social science, economics, statistical physics, and systems and control [1], [4], =-=[9]-=-, [10], [18], [16]. A comprehensive survey up to 2009 is available in [5]. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of others whic... |

142 | Distributed consensus algorithms in sensor networks: Link failures and channel noise
- Kar, Moura
- 2009
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Citation Context ... the structure of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to [2], [12], [13], [14], =-=[15]-=-, [17], [21]. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a framework of nonlinear stocha... |

89 |
Towards consensus: Some convergence theorems on repeated averaging
- Chatterjee, Seneta
- 1977
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Citation Context ...which is reflected by the decreasing step size. This algorithm shares some similarity to consensus algorithms with measurement noise [12], [13], [14], which have linear dynamics. The early works [7], =-=[6]-=- used decreasing step sizes in noiseless consensus problems to model hardening positions. We introduce the following assumptions. (A1) at > 0 for all t, å¥t=0 at = ¥, å ¥ t=0 a 2 t < ¥. (A2) For eac... |

82 | A discrete nonlinear and non-autonomous model of consensus formation
- Krause
- 2000
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Citation Context ...l opinion formation have attracted considerable interest of researchers in different areas including social science, economics, statistical physics, and systems and control [1], [4], [9], [10], [18], =-=[16]-=-. A comprehensive survey up to 2009 is available in [5]. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of others which are within a con... |

72 | Continuous opinion dynamics under bounded confidence: A survey
- Lorenz
- 2007
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Citation Context ... social opinion formation have attracted considerable interest of researchers in different areas including social science, economics, statistical physics, and systems and control [1], [4], [9], [10], =-=[18]-=-, [16]. A comprehensive survey up to 2009 is available in [5]. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of others which are within... |

57 | On krause’s multi-agent consensus model with state-dependent connectivity
- Blondel, Hendrickx, et al.
- 2009
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Citation Context ...N The studies on social opinion formation have attracted considerable interest of researchers in different areas including social science, economics, statistical physics, and systems and control [1], =-=[4]-=-, [9], [10], [18], [16]. A comprehensive survey up to 2009 is available in [5]. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of others... |

41 | Spread of (Mis)information in social networks
- Acemoglu, Ozdaglar, et al.
- 2010
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Citation Context ...UCTION The studies on social opinion formation have attracted considerable interest of researchers in different areas including social science, economics, statistical physics, and systems and control =-=[1]-=-, [4], [9], [10], [18], [16]. A comprehensive survey up to 2009 is available in [5]. Under the Hegselmann-Krause modeling [10], [16], agents simultaneously update their opinions by using opinions of o... |

32 |
Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior
- Huang, &Manton
- 2009
(Show Context)
Citation Context ...rmination of the structure of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to [2], [12], =-=[13]-=-, [14], [15], [17], [21]. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a framework of nonl... |

31 |
Decentralized parameter estimation by consensus based stochastic approximation
- Stankovic, Stankovic, et al.
- 2011
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Citation Context ...re of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to [2], [12], [13], [14], [15], [17], =-=[21]-=-. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a framework of nonlinear stochastic approxi... |

23 |
Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises, Automatic Control
- Li, Zhang
- 2010
(Show Context)
Citation Context ...tructure of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to [2], [12], [13], [14], [15], =-=[17]-=-, [21]. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a framework of nonlinear stochastic a... |

16 |
Stochastic consensus seeking with noisy and directed inter-agent communication: Fixed and randomly varying topologies
- Huang, Manton
- 2010
(Show Context)
Citation Context ...ion of the structure of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to [2], [12], [13], =-=[14]-=-, [15], [17], [21]. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a framework of nonlinear ... |

11 |
Approaching consensus can be delicate when positions harden. Stochastic Processes and their Applications 22
- JE, Hajnal, et al.
- 1986
(Show Context)
Citation Context ...ents which is reflected by the decreasing step size. This algorithm shares some similarity to consensus algorithms with measurement noise [12], [13], [14], which have linear dynamics. The early works =-=[7]-=-, [6] used decreasing step sizes in noiseless consensus problems to model hardening positions. We introduce the following assumptions. (A1) at > 0 for all t, å¥t=0 at = ¥, å ¥ t=0 a 2 t < ¥. (A2) Fo... |

11 | Social impact models of opinion dynamics
- Hølyst, Kacperski, et al.
(Show Context)
Citation Context ...he work [19] used shrinking confidence intervals and analyzed the formation and detection of communities. In the past research, some attention has been given to noisy opinion dynamics. The early work =-=[11]-=- applied additive noise to the learning rule [11]. The role of noise for more realistic modeling is also discussed in [5, pp. 610-611]. By introducing free will, an agent has positive probabilities to... |

9 | Opinion dynamics with decaying confidence: Application to community detection in graphs
- Morãrescu, Girard
(Show Context)
Citation Context ...es after some time, agents in different clusters cease to have effective opinion exchange. Some lower bound estimates of the inter-cluster distances in the steady state are developed in [4]. The work =-=[19]-=- used shrinking confidence intervals and analyzed the formation and detection of communities. In the past research, some attention has been given to noisy opinion dynamics. The early work [11] applied... |

5 | Stochastic approximation for consensus: a new approach via ergodic backward products
- Huang
- 2012
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Citation Context ...e determination of the structure of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to [2], =-=[12]-=-, [13], [14], [15], [17], [21]. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a framework o... |

4 |
M.: The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model. arXiv preprint arXiv:1208.2618
- Carro, Toral, et al.
- 2012
(Show Context)
Citation Context ...611]. By introducing free will, an agent has positive probabilities to have a jump in its opinion according to a certain distribution or perform an opinion learning rule using information from others =-=[3]-=-, [20]. This paper introduces a new stochastic noisy modeling of social opinion dynamics. The natural motivation is to consider the introduction of inaccuracies when the communication of opinions take... |

2 |
Approximate consensus in multi-agent stochastic systems with switched topology and noise
- Amelina, Fradkov, et al.
- 2012
(Show Context)
Citation Context ...is the determination of the structure of the equilibrium set of the associated nonlinear vector field. For the application of stochastic approximation to consensus problems, the reader is referred to =-=[2]-=-, [12], [13], [14], [15], [17], [21]. The paper is organized as follows. Section II describes the social opinion model with noisy information acquisition and bounded confidence, which leads to a frame... |

2 |
Diffusing opinions in bounded confidence processes
- Pineda, Toral, et al.
- 2011
(Show Context)
Citation Context ... By introducing free will, an agent has positive probabilities to have a jump in its opinion according to a certain distribution or perform an opinion learning rule using information from others [3], =-=[20]-=-. This paper introduces a new stochastic noisy modeling of social opinion dynamics. The natural motivation is to consider the introduction of inaccuracies when the communication of opinions takes plac... |