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Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice

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

Abstract

We investigate the spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps in coupling connections. Here, the coupling methods between lattices are both linear neighborhood coupling and the nonlinear chaotic map coupling of lattices. While strictly nearest neighborhood coupling is only a special case in the proposed system. We employed the criteria such as Kolmogorov–Sinai entropy density and universality, bifurcation diagrams, space–amplitude and space–time diagrams to investigate the chaotic behaviors of the proposed system in this paper. In fact, the proposed system contains new features for applications of cryptography such as the larger range of parameters for chaotic behaviors, the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic windows in bifurcation diagrams. Furthermore, we also show the parameter ranges of the proposed system which hold those features in cryptography compared with those of the CML system. Finally, we design the encryption scheme based on the proposed system for an explicit illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:402:y:2014:i:c:p:104-118
    DOI: 10.1016/j.physa.2014.01.051
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    References listed on IDEAS

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    Cited by:

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    2. Lu, Guangqing & Smidtaite, Rasa & Navickas, Zenonas & Ragulskis, Minvydas, 2018. "The Effect of Explosive Divergence in a Coupled Map Lattice of Matrices," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 308-313.
    3. Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    4. 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).
    5. Liang, Bo & Hu, Chenyang & Tian, Zean & Wang, Qiao & Jian, Canling, 2023. "A 3D chaotic system with multi-transient behavior and its application in image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    6. Sun, Yu-jie & Zhang, Hao & Wang, Xing-yuan & Wang, Xiao-qing & Yan, Peng-fei, 2020. "2D Non-adjacent coupled map lattice with q and its applications in image encryption," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    7. dos Santos, Vagner & Szezech Jr., José D. & Baptista, Murilo S. & Batista, Antonio M. & Caldas, Iberê L., 2016. "Unstable dimension variability structure in the parameter space of coupled Hénon maps," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 23-28.

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