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<p>We introduce discrete and <i>p</i>-adic continuous versions of the Schnakenberg system on a one-dimensional <i>p</i>-adic unit ball. We establish criteria for the existence of Turing patterns in <i>p</i>-adic Schnakenberg systems. We give extensive simulations of some of these systems. We present numerical simulations that illustrate the shape of the Turing patterns in our system on the <i>p</i>-adic unit ball. Finally, we compare the numerical solution obtained in a specific Schnakenberg system in the classical case with the numerical solution obtained in a particular Schnakenberg system in the <i>p</i>-adic case.</p>

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Formation of Turing patterns in the Schnakenberg system over the p-adic integers

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • C. A. Garcia-Bibiano,
  • L. F. Chacón-Cortés

摘要

We introduce discrete and p-adic continuous versions of the Schnakenberg system on a one-dimensional p-adic unit ball. We establish criteria for the existence of Turing patterns in p-adic Schnakenberg systems. We give extensive simulations of some of these systems. We present numerical simulations that illustrate the shape of the Turing patterns in our system on the p-adic unit ball. Finally, we compare the numerical solution obtained in a specific Schnakenberg system in the classical case with the numerical solution obtained in a particular Schnakenberg system in the p-adic case.