American Institute of Mathematical Sciences

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2004, 1(2): 347-359. doi: 10.3934/mbe.2004.1.347

Communication and Synchronization in Disconnected Networks with Dynamic Topology: Moving Neighborhood Networks

Joseph D. Skufca 1, and  Erik M. Bollt 2,

1. 

Department of Mathematics, United States Naval Academy, Annapolis, MD 21402, United States
2. 

Deptartments of Mathematics, Computer Science, and Physics, Clarkson University, Potsdam, NY 13699, United States

Received  April 2004 Revised  June 2004 Published  July 2004

We consider systems that are well modelled as networks that evolve in time, which we call Moving Neighborhood Networks. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent interactions arise from ad hoc networks. In a natural way, the time-averaged degree distribution gives rise to a scale-free network. Simulations show that although the network may have many noncommunicating components, the recent weighted time-averaged communication is sufficient to yield robust synchronization of chaotic oscillators. In particular, we contend that such time-varying networks are important to model in the situation where each agent carries a pathogen (such as a disease) in which the pathogen's life-cycle has a natural time-scale which competes with the time-scale of movement of the agents, and thus with the networks communication channels.
Keywords: communication in complex networks., mathematical model, Disease spread in communities, nonlinear dynamics, self-organization, epidemiology.
Mathematics Subject Classification: 92D30, 37A25, 37D45, 37N25, 05C8.
Citation: Joseph D. Skufca, Erik M. Bollt. Communication and Synchronization in Disconnected Networks with Dynamic Topology: Moving Neighborhood Networks. Mathematical Biosciences & Engineering, 2004, 1 (2) : 347-359. doi: 10.3934/mbe.2004.1.347
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