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Complexity analysis of network-based dynamical systems

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Abstract

This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.

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Author information

Authors and Affiliations

  1. School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Guofeng Zhang

  2. Intelligent Control Laboratory, Center for Systems and Control, College of Engineering, Peking University, Beijing, 100871, China

    Long Wang

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, T6G 2V 4, Canada

    Tongwen Chen

Authors
  1. Guofeng Zhang
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  2. Long Wang
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  3. Tongwen Chen
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Corresponding author

Correspondence to Guofeng Zhang.

Additional information

This research of the first author is partially supported by an the National Natural Science Foundation of China under Grant No. 60804015, and an NSERC grant to the third author.

This paper was recommended for publication by Editor Jing HAN.

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Zhang, G., Wang, L. & Chen, T. Complexity analysis of network-based dynamical systems. J Syst Sci Complex 24, 413–432 (2011). https://doi.org/10.1007/s11424-011-8173-6

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  • DOI: https://doi.org/10.1007/s11424-011-8173-6

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