Turing Patterns in a

$$p$$

-Adic FitzHugh-Nagumo System on the Unit Ball

Abstract We introduce discrete and

$$p$$

-adic continuous versions of the FitzHugh-Nagumo system on the one-dimensional

$$p$$

-adic unit ball. We provide criteria for the existence of Turing patterns. We present extensive simulations of some of these systems. The simulations show that the Turing patterns are traveling waves in the

$$p$$

-adic unit ball.