An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems

This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, \(\textit{m}\) $\mathit{m}$ and \(\textit{m}\) $\mathit{m}$ + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.