Turing Stability and Natural Pattern Formation in the Gray-Scott Reaction-Diffusion System

Authors

  • K. Fahad Mia Department of Computer Science & Engineering, National Institute of Textile Engineering and Research (NITER), Nayarhat, Savar, Dhaka, Bangladesh
  • Md. Jakaria Hossen Shikder Department of Science and Humanities, Military Institute of Science and Technology (MIST), Mirpur-12, Dhaka-1216, Bangladesh
  • Nasiruddin M. Himel Department of Electrical, Electronic and Communication Engineering, Military Institute of Science and Technology (MIST), Mirpur-12, Dhaka-1216, Bangladesh
  • M. M. Rahman Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh

DOI:

https://doi.org/10.18034/ei.v12i1.750

Keywords:

Reaction-Diffusion Systems, Turing Stability, Gray-Scott Model, Pattern Formation, Nonlinear Dynamics, Mathematical Biology

Abstract

This paper examines the Gray-Scott model, a coupled system of nonlinear reaction-diffusion equations recognized for its capacity to produce intricate patterns. Our focus is on performing a Turing stability analysis to understand the conditions under which spatially heterogeneous structures emerge. By exploring the dynamics of the model under various parameter regimes, we demonstrate how the resulting patterns closely resemble those found in nature, such as animal coat markings, seashell textures, and chemical oscillations. The sensitivity of the model to its parameters reveals a rich spectrum of behavior, highlighting the profound connection between mathematical models and natural pattern formation.

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References

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Published

2024-06-30

Issue

Section

Peer Reviewed Articles

How to Cite

Mia, K. F., Shikder, M. J. H., Himel, N. M., & Rahman, M. M. (2024). Turing Stability and Natural Pattern Formation in the Gray-Scott Reaction-Diffusion System. Engineering International, 12(1), 83-96. https://doi.org/10.18034/ei.v12i1.750

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