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Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

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  • Khellat, Farhad
  • Ghaderi, Akashe
  • Vasegh, Nastaran

Abstract

This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li–Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 22-cycles are also shown by simulations for some values of the parameters.

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  • Khellat, Farhad & Ghaderi, Akashe & Vasegh, Nastaran, 2011. "Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 934-939.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:11:p:934-939
    DOI: 10.1016/j.chaos.2011.07.015
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    References listed on IDEAS

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    1. M. K. Ali & Jin-Qing Fang, 1997. "Synchronization of spatiotemporal chaos using nonlinear feedback functions," Discrete Dynamics in Nature and Society, Hindawi, vol. 1, pages 1-6, January.
    2. Gardini, Laura & Sushko, Iryna & Avrutin, Viktor & Schanz, Michael, 2011. "Critical homoclinic orbits lead to snap-back repellers," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 433-449.
    3. Herrera, Ma Dolores Sotelo & Martín, Jesús San, 2009. "An analytical study in coupled map lattices of synchronized states and traveling waves, and of their period-doubling cascades," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 901-910.
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    Cited by:

    1. Zhang, Ying-Qian & He, Yi & Wang, Xing-Yuan, 2018. "Spatiotemporal chaos in mixed linear–nonlinear two-dimensional coupled logistic map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 148-160.
    2. Wang, Xingyuan & Yang, Jingjing, 2021. "Spatiotemporal chaos in multiple coupled mapping lattices with multi-dynamic coupling coefficient and its application in color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Wang, Xingyuan & Du, Xiaohui, 2022. "Pixel-level and bit-level image encryption method based on Logistic-Chebyshev dynamic coupled map lattices," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Liang, Wei & Lv, Xiaolin, 2022. "Li-Yorke chaos in a class of controlled delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Wang, Mingxu & Wang, Xingyuan & Wang, Chunpeng & Xia, Zhiqiu & Zhao, Hongyu & Gao, Suo & Zhou, Shuang & Yao, Nianmin, 2020. "Spatiotemporal chaos in cross coupled map lattice with dynamic coupling coefficient and its application in bit-level color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Zhang, Ying-Qian & Wang, Xing-Yuan, 2014. "Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 104-118.
    7. Wang, Xingyuan & Yang, Jingjing & Guan, Nana, 2021. "High-sensitivity image encryption algorithm with random cross diffusion based on dynamically random coupled map lattice model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Zhao, Hongyu & Wang, Shengsheng & Wang, Xingyuan, 2022. "Fast image encryption algorithm based on multi-parameter fractal matrix and MPMCML system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Wang, Xingyuan & Xue, Wenhua & An, Jubai, 2020. "Image encryption algorithm based on Tent-Dynamics coupled map lattices and diffusion of Household," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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