Distributed averaging under constraints on information exchange: Emergence of lévy flights

Jing Wang, Nicola Elia

Research output: Contribution to journalArticle

41 Scopus citations


In this paper, we study the fragility of a popular distributed averaging algorithm when the information exchange among the nodes is limited by communication delays, fading connections and additive noise. We show that the otherwise well studied and benign multi-agent system can generate a collective global complex behavior. We characterize this behavior, common to many natural and human-made interconnected systems, as a collective hyper-jump diffusion process and as a Lévy flight process in a special case. We further describe the mechanism for its emergence and predict its occurrence, under standard assumptions, by checking the Mean Square instability of a certain part of the system. We show that the strong connectivity property of the network topology guarantees that the complex behavior is global and manifested by all the agents in the network, even though the source of uncertainty is localized.

Original languageEnglish (US)
Article number6144712
Pages (from-to)2435-2449
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - Sep 18 2012
Externally publishedYes


  • Complex systems
  • Lévy flights
  • distributed averaging
  • distributed consensus
  • hyper-jump diffusion processes
  • mean square stability
  • networked systems

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