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In silico investigation of the formation of multiple intense zebra stripes using extending domain

Author

Listed:
  • Kim, Hyundong
  • Jyoti,
  • Kwak, Soobin
  • Ham, Seokjun
  • Kim, Junseok

Abstract

We perform an in silico investigation of the formation of multiple intense zebra stripes by extending the domain with an appropriate extending speed. The common zebra has alternating dark and light stripes, creating a two phase pattern. However, some Equus burchelli zebras have an intermediate gray color stripe situated between the dark and light stripes. To numerically investigate the formation of multiple intense zebra stripes, we first find the equilibrium state of the governing system in the one-dimensional (1D) static domains using various frequency modes. After finding the equilibrium state for the governing system in the 1D static domains, we stack a numerical data. Then, we load the stacked numerical data to use as an initial state for finding the growth rate that forms the multiple intense zebra stripe formation in the 1D extended domains. Next, convergence experiments are conducted to verify the convergence of the numerical method for the governing system. Finally, numerical simulations are performed to confirm the formation of multiple intense zebra stripes in two-dimensional extending domains and on evolving curved surfaces.

Suggested Citation

  • Kim, Hyundong & Jyoti, & Kwak, Soobin & Ham, Seokjun & Kim, Junseok, 2024. "In silico investigation of the formation of multiple intense zebra stripes using extending domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 648-658.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:648-658
    DOI: 10.1016/j.matcom.2024.06.010
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    References listed on IDEAS

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    1. Wu, Daiyong & Yang, Youwei & Wu, Peng, 2023. "Impacts of prey-taxis and nonconstant mortality on a spatiotemporal predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 283-300.
    2. 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.
    3. 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).
    4. Banda, Heather & Chapwanya, Michael & Dumani, Phindile, 2022. "Pattern formation in the Holling–Tanner predator–prey model with predator-taxis. A nonstandard finite difference approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 336-353.
    5. Tim Caro & Amanda Izzo & Robert C. Reiner & Hannah Walker & Theodore Stankowich, 2014. "The function of zebra stripes," Nature Communications, Nature, vol. 5(1), pages 1-10, May.
    6. Ham, Seokjun & Kim, Junseok, 2023. "Stability analysis for a maximum principle preserving explicit scheme of the Allen–Cahn equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 453-465.
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