Global Theoretical Investigation of Diffusion Driven Instability for Three Coupled Equations of a Reaction Diffusion System
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Date
2026
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Abstract
Abstract: In this paper, we investigate the mechanism called DDI ( Diffusion Driven
Instability) for a full three dimensional matrix of diffusion coefficients. We apply
a linear approach in the neighborhood of an arbitrary equilibrium point using the
Routh-Hurwitz stability criterion and we study the existence of at least one eigenvalue
with positive real part of the matrix A(k). Our main result is the proof of sufficient
and necessary condition for the Turing instability. The research is extended to a
reaction-diffusion system for three species.