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Spatiotemporal chaos in mixed linear–nonlinear two-dimensional coupled logistic map lattice

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  • Zhang, Ying-Qian
  • He, Yi
  • Wang, Xing-Yuan

Abstract

We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov–Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:148-160
    DOI: 10.1016/j.physa.2017.07.019
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    References listed on IDEAS

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    1. Vasconcelos, D.B. & Viana, R.L. & Lopes, S.R. & Pinto, S.E. de S., 2006. "Conversion of local transient chaos into global laminar states in coupled map lattices with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 158-172.
    2. de Pontes, José C.A. & Batista, Antônio M. & Viana, Ricardo L. & Lopes, Sérgio R., 2006. "Self-organized memories in coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 387-398.
    3. 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.
    4. Pandit, Rahul & Pande, Ashwin & Sinha, Sitabhra & Sen, Avishek, 2002. "Spiral turbulence and spatiotemporal chaos: characterization and control in two excitable media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 306(C), pages 211-219.
    5. dos Santos, A.M. & Viana, R.L. & Lopes, S.R. & de S. Pinto, S.E. & Batista, A.M., 2008. "Collective behavior in coupled chaotic map lattices with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1655-1668.
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    Cited by:

    1. Limei Liu & Xitong Zhong, 2024. "Research on Stability and Bifurcation for Two-Dimensional Two-Parameter Squared Discrete Dynamical Systems," Mathematics, MDPI, vol. 12(15), pages 1-20, August.
    2. Yao, Xiao-Yue & Li, Xian-Feng & Jiang, Jun & Leung, Andrew Y.T., 2022. "Codimension-one and -two bifurcation analysis of a two-dimensional coupled logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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