= Negative self-response excludes two-species Turing instability
For a reaction-stable two-species <equilibrium> with both <Jacobian matrix> diagonal entries negative and positive diagonal diffusivities, each spatial mode has more negative <trace> after <diffusion> is added. Its <determinant> is the positive reaction <determinant> plus positive coefficients of $k^2$ and $k^4$. Hence every mode stays stable. Unequal <diffusion> alone is insufficient for a <Turing instability>; the reaction feedback must also permit a destabilizing weighted diagonal sum.
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