# Pattern formation in nonlocal Kondo model

## TL;DR

This paper investigates a nonlocal evolution equation inspired by Kondo's model to explain color pattern formation on guppy fish skin, proving stationary solutions and demonstrating pattern similarities with reaction-diffusion systems.

## Contribution

It introduces a nonlocal model for pattern formation, proving existence of solutions and showing numerical patterns akin to classical reaction-diffusion models.

## Key findings

- Existence of stationary solutions established.
- Numerical simulations show pattern formation.
- Patterns resemble those in reaction-diffusion equations.

## Abstract

We study a nonlocal evolution equation generalising a model introduced by Shigeru Kondo to explain colour patterns on a skin of a guppy fish. We prove the existence of stationary solutions using either the bifurcation theory or the Schauder fixed point theorem. We also present numerical studies of this model and show that it exhibits patterns similar to those modelled by well-known reaction-diffusion equations.