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Numerical simulation of the zebra pattern formation on a three-dimensional model

Author

Listed:
  • Jeong, Darae
  • Li, Yibao
  • Choi, Yongho
  • Yoo, Minhyun
  • Kang, Dooyoung
  • Park, Junyoung
  • Choi, Jaewon
  • Kim, Junseok

Abstract

In this paper, we numerically investigate the zebra skin pattern formation on the surface of a zebra model in three-dimensional space. To model the pattern formation, we use the Lengyel–Epstein model which is a two component activator and inhibitor system. The concentration profiles of the Lengyel–Epstein model are obtained by solving the corresponding reaction–diffusion equation numerically using a finite difference method. We represent the zebra surface implicitly as the zero level set of a signed distance function and then solve the resulting system on a discrete narrow band domain containing the zebra skin. The values at boundary are dealt with an interpolation using the closet point method. We present the numerical method in detail and investigate the effect of the model parameters on the pattern formation on the surface of the zebra model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:475:y:2017:i:c:p:106-116
    DOI: 10.1016/j.physa.2017.02.014
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    References listed on IDEAS

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    1. dos S. Silva, F.A. & Viana, R.L. & Lopes, S.R., 2015. "Pattern formation and Turing instability in an activator–inhibitor system with power-law coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 487-497.
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    Cited by:

    1. 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).
    2. Jeong, Darae & Li, Yibao & Choi, Yongho & Lee, Chaeyoung & Yang, Junxiang & Kim, Junseok, 2021. "A practical adaptive grid method for the Allen–Cahn equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

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