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

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.