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Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits

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Abstract

In this paper, a certain kind of intermittent scheme is used to control the chaos in a single chaotic Chua circuit to reach an arbitrary orbit. Furthermore, it is confirmed to be effective in suppressing spatiotemporal chaos and a spiral wave in the networks of Chua circuits with nearest-neighbor connections. The controllable and measurable variable is sampled, and the linear error between the sampled variable and the selected thresholds is fed back into the system only if the sampled variable exceeds the thresholds; otherwise, the system will develop itself without any external perturbation. In experiments, the control scheme could be realized by using the Heavside function. In the case of one single chaotic Chua circuit, the chaotic state can be controlled to reach an arbitrary n-periodical orbit (n=1,2,3,5,6,…) with appropriate feedback intensity and thresholds. It is argued that this scheme could explain the mechanism of what is called phase compression. Then the phase compression scheme is used to control a spiral wave and spatiotemporal chaos in a network of Chua circuits with 256×256 sites. The numerical simulation results confirm its effectiveness when appropriate upper and bottom thresholds are used by monitoring the measurable output voltages of the chaotic circuit in one site of the network.

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Authors and Affiliations

  1. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Chun-Ni Wang, Jun Ma & Long Huang

  2. Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou, 730050, China

    Jun Ma

  3. School of Mathematical Science, Yancheng Teacher’s University, Yancheng, 224051, China

    Yong Liu

Authors
  1. Chun-Ni Wang
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  2. Jun Ma
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  3. Yong Liu
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  4. Long Huang
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Correspondence to Jun Ma.

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Wang, CN., Ma, J., Liu, Y. et al. Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits. Nonlinear Dyn 67, 139–146 (2012). https://doi.org/10.1007/s11071-011-9965-x

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  • DOI: https://doi.org/10.1007/s11071-011-9965-x

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