Random talk: Random walk and synchronizability in a moving neighborhood network

Maurizio Porfiri, Daniel J. Stilwell, Erik M. Bollt, Joseph D. Skufca

Research output: Contribution to journalArticlepeer-review


We examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network. Each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator. The communication network topology changes randomly and is dictated by the agents' locations in the lattice. Information sharing (talking) is possible only for geographically neighboring agents. This complex system is a time-varying jump nonlinear system. We introduce the concept of 'long-time expected communication network', defined as the ergodic limit of a stochastic time-varying network. We show that if the long-time expected network supports synchronization, then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice.

Original languageEnglish (US)
Pages (from-to)102-113
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - Dec 2006


  • Fast switching
  • Graph
  • Random walk
  • Stochastic stability
  • Synchronization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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