# Pattern formation driven by cross--diffusion in a 2D domain

Source: [Pattern formation driven by cross--diffusion in a 2D domain](<https://www.sota2.com/research/paper/68fa2d1a1e209131ce856972>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T15:47:29.177Z

Authors: G.Gambino, M. C. Lombardo, M. Sammartino

Published: 2012-11-19T13:36:23.000Z

## Abstract

In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, hexagonal patterns.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1211.4412>)

[PDF](<https://arxiv.org/pdf/1211.4412.pdf>)