= Equal-diffusivity Fisher reduction
{title2=$v=1-u,\quad\beta=1-\delta$}
In $u_t=u(1-u-\beta v)+u_{xx}$, $v_t=-\delta uv+v_{xx}$, the line $v=1-u$ is invariant when $\beta=1-\delta$. On it $u$ satisfies <Fisher's equation> with growth coefficient $\delta$. The reduction also requires compatible initial and boundary data: parameter tuning alone does not reduce arbitrary two-field solutions. Positive <concentrations> and positive $\beta$ in this normalization require $0<\delta<1$.
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