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

92D30, 37A25, 37D45, 37N25, 05C80.

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

1. Department of Mathematics, United States Naval Academy, Annapolis, MD 21402
2. Deptartments of Mathematics, Computer Science, and Physics, Clarkson University, Potsdam, NY 13699

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.
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Keywords communication in complex networks.; mathematical model; Disease spread in communities; nonlinear dynamics; self-organization; epidemiology

Citation: Joseph D. Skufca, Erik M. Bollt. Communication and Synchronization in Disconnected Networks with Dynamic Topology: Moving Neighborhood Networks. Mathematical Biosciences and Engineering, 2004, 1(2): 347-359. doi: 10.3934/mbe.2004.1.347

 

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Copyright Info: 2004, Joseph D. Skufca, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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