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Computer simulation of the nonhomogeneous zebra pattern formation using a mathematical model with space-dependent parameters

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  • Yang, Junxiang
  • Kim, Junseok

Abstract

In this study, we present a mathematical model with space-dependent parameters and appropriate boundary conditions which can simulate the realistic nonhomogeneous zebra pattern formation. The proposed model is based on the Lengyel–Epstein (LE) model and the finite difference method is used to solve the governing equation with appropriate boundary and initial conditions on a complex zebra domain. We focus on generating nonhomogeneous pattern of the common plains zebra (E. burchelli), which is geographically widespread species of zebra. Using the space-dependent parameters in the model, we can simulate the zebra pattern formation with various width stripes.

Suggested Citation

  • Yang, Junxiang & Kim, Junseok, 2023. "Computer simulation of the nonhomogeneous zebra pattern formation using a mathematical model with space-dependent parameters," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001509
    DOI: 10.1016/j.chaos.2023.113249
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    References listed on IDEAS

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    1. Gulati, Pankaj & Chauhan, Sudipa & Mubayi, Anuj & Singh, Teekam & Rana, Payal, 2021. "Dynamical analysis, optimum control and pattern formation in the biological pest (EFSB) control model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Corina E. Tarnita & Juan A. Bonachela & Efrat Sheffer & Jennifer A. Guyton & Tyler C. Coverdale & Ryan A. Long & Robert M. Pringle, 2017. "A theoretical foundation for multi-scale regular vegetation patterns," Nature, Nature, vol. 541(7637), pages 398-401, January.
    3. Jeong, Darae & Li, Yibao & Choi, Yongho & Yoo, Minhyun & Kang, Dooyoung & Park, Junyoung & Choi, Jaewon & Kim, Junseok, 2017. "Numerical simulation of the zebra pattern formation on a three-dimensional model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 106-116.
    4. Owolabi, Kolade M., 2021. "Computational analysis of different Pseudoplatystoma species patterns the Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Liu, Haicheng & Ge, Bin, 2022. "Turing instability of periodic solutions for the Gierer–Meinhardt model with cross-diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
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    1. Yang, Junxiang & Lee, Dongsun & Kwak, Soobin & Ham, Seokjun & Kim, Junseok, 2024. "The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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