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Oscillation and chaos in a deterministic traffic network

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  • Xia, Yongxiang
  • Liu, Nianjun
  • Iu, Herbert H.C.

Abstract

Traffic dynamics of regular networks are of importance in theory and practice. In this paper, we study such a problem with a regular lattice structure. We specify the network structure and traffic protocols so that all the random features are removed. When a node is attacked and then removed, the traffic redistributes, causing complicated dynamical results. With different system redundancy, we observe rich dynamics, ranging from stable state to periodic to chaotic oscillation. Since this is a completely deterministic system, we can conclude that the nonlinear dynamics is purely due to the interior nonlinear feature of the traffic.

Suggested Citation

  • Xia, Yongxiang & Liu, Nianjun & Iu, Herbert H.C., 2009. "Oscillation and chaos in a deterministic traffic network," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1700-1704.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1700-1704
    DOI: 10.1016/j.chaos.2009.03.097
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    References listed on IDEAS

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    1. Jenelius, Erik & Petersen, Tom & Mattsson, Lars-Göran, 2006. "Importance and exposure in road network vulnerability analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(7), pages 537-560, August.
    2. Li, Ping & Yi, Zhang & Zhang, Lei, 2006. "Global synchronization of a class of delayed complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 903-908.
    3. Lu, Jianquan & Ho, Daniel W.C., 2008. "Local and global synchronization in general complex dynamical networks with delay coupling," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1497-1510.
    4. M. T. Gastner & M. E.J. Newman, 2006. "The spatial structure of networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(2), pages 247-252, January.
    5. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
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    Cited by:

    1. Mukherjee, Somenath & Ray, Rajdeep & Samanta, Rajkumar & Khondekar, Mofazzal H. & Sanyal, Goutam, 2017. "Nonlinearity and chaos in wireless network traffic," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 23-29.
    2. Zhou, Jian & Coit, David W. & Felder, Frank A. & Wang, Dali, 2021. "Resiliency-based restoration optimization for dependent network systems against cascading failures," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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