American Institute of Mathematical Sciences

Advanced
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
[1]

Razvan C. Fetecau, Beril Zhang. Self-organization on Riemannian manifolds. Journal of Geometric Mechanics, 2019, 11 (3) : 397-426. doi: 10.3934/jgm.2019020
[2]

Suoqin Jin, Fang-Xiang Wu, Xiufen Zou. Domain control of nonlinear networked systems and applications to complex disease networks. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2169-2206. doi: 10.3934/dcdsb.2017091
[3]

Meihong Qiao, Anping Liu, Qing Tang. The dynamics of an HBV epidemic model on complex heterogeneous networks. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1393-1404. doi: 10.3934/dcdsb.2015.20.1393
[4]

Jianquan Li, Yicang Zhou, Jianhong Wu, Zhien Ma. Complex dynamics of a simple epidemic model with a nonlinear incidence. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 161-173. doi: 10.3934/dcdsb.2007.8.161
[5]

Karen R. Ríos-Soto, Baojun Song, Carlos Castillo-Chavez. Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 199-222. doi: 10.3934/mbe.2011.8.199
[6]

W. E. Fitzgibbon, J. J. Morgan. Analysis of a reaction diffusion model for a reservoir supported spread of infectious disease. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 6239-6259. doi: 10.3934/dcdsb.2019137
[7]

Wendi Wang. Population dispersal and disease spread. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 797-804. doi: 10.3934/dcdsb.2004.4.797
[8]

Ionel S. Ciuperca, Matthieu Dumont, Abdelkader Lakmeche, Pauline Mazzocco, Laurent Pujo-Menjouet, Human Rezaei, Léon M. Tine. Alzheimer's disease and prion: An in vitro mathematical model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5225-5260. doi: 10.3934/dcdsb.2019057
[9]

S.M. Moghadas. Modelling the effect of imperfect vaccines on disease epidemiology. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 999-1012. doi: 10.3934/dcdsb.2004.4.999
[10]

Louis D. Bergsman, James M. Hyman, Carrie A. Manore. A mathematical model for the spread of west nile virus in migratory and resident birds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 401-424. doi: 10.3934/mbe.2015009
[11]

David Greenhalgh, Karen E. Lamb, Chris Robertson. A mathematical model for the spread of streptococcus pneumoniae with transmission due to sequence type. Conference Publications, 2011, 2011 (Special) : 553-567. doi: 10.3934/proc.2011.2011.553
[12]

Georgy P. Karev. Dynamics of heterogeneous populations and communities and evolution of distributions. Conference Publications, 2005, 2005 (Special) : 487-496. doi: 10.3934/proc.2005.2005.487
[13]

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods. Kinetic & Related Models, 2017, 10 (1) : 1-32. doi: 10.3934/krm.2017001
[14]

Marco Sarich, Natasa Djurdjevac Conrad, Sharon Bruckner, Tim O. F. Conrad, Christof Schütte. Modularity revisited: A novel dynamics-based concept for decomposing complex networks. Journal of Computational Dynamics, 2014, 1 (1) : 191-212. doi: 10.3934/jcd.2014.1.191
[15]

Shouying Huang, Jifa Jiang. Epidemic dynamics on complex networks with general infection rate and immune strategies. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2071-2090. doi: 10.3934/dcdsb.2018226
[16]

Jiying Ma, Dongmei Xiao. Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2377-2396. doi: 10.3934/dcdsb.2013.18.2377
[17]

Stelian Ion, Gabriela Marinoschi. A self-organizing criticality mathematical model for contamination and epidemic spreading. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 383-405. doi: 10.3934/dcdsb.2017018
[18]

Junyuan Yang, Yuming Chen, Jiming Liu. Stability analysis of a two-strain epidemic model on complex networks with latency. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2851-2866. doi: 10.3934/dcdsb.2016076
[19]

Ali Unver, Christian Ringhofer, Dieter Armbruster. A hyperbolic relaxation model for product flow in complex production networks. Conference Publications, 2009, 2009 (Special) : 790-799. doi: 10.3934/proc.2009.2009.790
[20]

Wenzhang Huang, Maoan Han, Kaiyu Liu. Dynamics of an SIS reaction-diffusion epidemic model for disease transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 51-66. doi: 10.3934/mbe.2010.7.51

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences