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Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications
Open accessAbstract
We study a simple continuous-time multiagent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergence to a set of clusters, with the agents in each cluster sharing a common value, and provide a lower bound on the distance between clusters at a stable equilibrium, under a suitable notion of multiagent system stability. To better understand the behavior of the system for a large number of agents, we introduce a variant involving a continuum of agents. We prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a nontrivial lower bound on the distance between clusters. Finally, we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents.
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Cites
Consensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522 · cited 1×
“Similar behaviors are observed for other distributions; see [9] for some more numerical experiments.”
BackgroundCoordination of groups of mobile autonomous agents using nearest neighbor rules
Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339
Cited by
A tutorial on modeling and analysis of dynamic social networks. Part I
Proskurnikov, A. V., & Tempo, R. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.03.002 · Cited by 553
A tutorial on modeling and analysis of dynamic social networks. Part II
Proskurnikov, A. V., & Tempo, R. (2018) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2018.03.005 · Cited by 294
Opinion Dynamics: Models, Extensions and External Effects
Sîrbu, A., Loreto, V., Servedio, V. D. P., & Tria, F. (2017) · Understanding Complex Systems · doi:10.1007/978-3-319-25658-0_17 · Cited by 186
Distributed multi-agent optimization with state-dependent communication
Lobel, I., Ozdaglar, A., & Feijer, D. (2011) · Mathematical Programming · doi:10.1007/s10107-011-0467-x · Cited by 162
Metadata
- Authors
- Blondel, V. D., Hendrickx, J. M., & Tsitsiklis, J. N.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 2010-01
- Volume
- 48
- Issue
- 8
- Pages
- 5214-5240
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2022149728
- Cited by
- 211
- References
- 2
- FWCI
- 8.78
- Type
- journal article
- Language
- en
- Open access
- green
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- Blondel, V. D., Hendrickx, J. M., & Tsitsiklis, J. N. (2010). Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications. SIAM Journal on Control and Optimization. https://doi.org/10.1137/090766188
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