Abstract
This paper explores a general strategy for analyzing network-based dynamical systems. The starting point is a method for parsing an arbitrary sequence of graphs over a given set of nodes. The technique is then harnessed to carry out a dynamic form of renormalization for averaging-based systems. This analytical framework allows us to formulate new criteria for ensuring the asymptotic periodicity of diffusive influence systems.
This work was supported in part by NSF grants CCF-0963825 and CCF-1420112. Part of it was done when the author was an Addie and Harold Broitman Member at the Institute for Advanced Study, Princeton, NJ.
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References
Bhattacharyya, A., Braverman, M., Chazelle, B., Nguyen, H.L.: On the convergence of the Hegselmann-Krause system. In: Proc. 4th ITCS, pp. 61–66 (2013)
Bullo, F., Cortés, J., Martinez, S.: Distributed Control of Robotic Networks, Applied Mathematics Series. Princeton University Press (2009)
Buluc, A., Meyerhenke, H., Safro, I., Sanders, P., Schulz, C.: Recent advances in graph partitioning. arXiv:1311.3144 (preprint)
Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)
Chazelle, B.: The total \(s\)-energy of a multiagent system. SIAM J. Control Optim. 49, 1680–1706 (2011)
Chazelle, B.: The dynamics of influence systems. In: Proc. 53rd IEEE FOCS, 311–320 (2012); To appear in J. SIAM Comput. (2014)
Chazelle, B.: An Algorithmic Approach to Collective Behavior. Journal of Statistical Physics 158, 514–548 (2015)
Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)
Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artificial Societies and Social Simulation 5, 3 (2002)
Hendrickx, J.M., Blondel, V.D.: Convergence of different linear and non-linear Vicsek models. In: Proc. 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, pp. 1229–1240, July 2006
Kempe, D., Kleinberg, J.M., Kumar, A.: Connectivity and inference problems for temporal networks. Journal of Computer and System Sciences 64, 820–842 (2002)
Lorenz, J.: A stabilization theorem for dynamics of continuous opinions. Physica A: Statistical Mechanics and its Applications 355, 217–223 (2005)
MartÃnez, S., Bullo, F., Cortés, J., Frazzoli, E.: On synchronous robotic networks Part ii: Time complexity of rendezvous and deployment algorithms. IEEE Transactions on Automatic Control 52, 2214–2226 (2007)
Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 50, 169–182 (2005)
Touri, B., Nedić, A.: Discrete-time opinion dynamics. In: Proc. 45th IEEE Asilomar Conference on Signals, Systems, and Computers, pp. 1172–1176 (2011)
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Chazelle, B. (2015). Communication, Dynamics, and Renormalization. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_1
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DOI: https://doi.org/10.1007/978-3-319-18173-8_1
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