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Pattern formation and Turing instability in an activator–inhibitor system with power-law coupling

Author

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  • dos S. Silva, F.A.
  • Viana, R.L.
  • Lopes, S.R.

Abstract

We investigate activator–inhibitor systems in two spatial dimensions with a non-local coupling, for which the interaction strength decreases with the lattice distance as a power-law. By varying a single parameter we can pass from a local (Laplacian) to a global (all-to-all) coupling type. We derived, from a linear stability analysis of the Fourier spatial modes, a set of conditions for the occurrence of a Turing instability, by which a spatially homogeneous pattern can become unstable. In nonlinear systems the growth of these modes is limited and pattern formation is possible. We have studied some qualitative features of the patterns formed in non-local coupled activator–inhibitor systems described by the Meinhardt–Gierer equations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:419:y:2015:i:c:p:487-497
    DOI: 10.1016/j.physa.2014.09.059
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    Cited by:

    1. Owolabi, Kolade M. & Karaagac, Berat, 2020. "Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    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. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.
    4. Wu, Ranchao & Zhou, Yue & Shao, Yan & Chen, Liping, 2017. "Bifurcation and Turing patterns of reaction–diffusion activator–inhibitor model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 597-610.

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