Table 2.

Numerical scales of various non-dimensional parameters and parameter groupings, motivated by the physical scales of synthetic pattern formation with E. coli bacterial colonies, in the studies of Grant et al. (2016) and Boehm et al. (2018). For matrices, the infinity (max) norm ${\Vert ·\Vert }_{\infty }$ is used, which is the modulus of the matrix component with largest magnitude. For the non-dimensional matrix Jacobian, this norm is taken to be of order unity as the timescale is non-dimensionalized relative to $\tau$, a representative timescale associated with a fast reaction in the system. The non-dimensional lengthscale, $\tilde{L}$, is retained symbolically throughout the presentation to facilitate determining the impact of this scale, though it is unity for these scalings. The parameter scales ${\epsilon }_{\ast }$ and $h_{\ast }$ as well as the range of ${\epsilon }_{\ast }^2/3$ are presented as they will be important in the asymptotic analyses below

Parameter	Typical value/range
$\epsilon =H_{\epsilon }/\widehat{L}$	$4.5\times {10}^{-4}-1.3\times {10}^{-2}$
$h=H/\widehat{L}$	$0.045-1.3$
$\tilde{L}=L/\widehat{L}$	1
${\epsilon }_{\ast }=\epsilon {\Vert {{\mathit{D}}_{\mathit{S}}}^{-1}\mathit{J}\Vert }_{\infty }^{1/2}$	$1.1\times {10}^{-3}-0.87$
$h_{\ast }=h{\Vert {{\mathit{D}}_{\mathit{S}}}^{-1}\mathit{J}\Vert }_{\infty }^{1/2}$	$0.11-87$
${\epsilon }_{\ast }^2/3$	$4.0\times {10}^{-7}-0.3$
${\Vert {\mathit{D}}_{\mathit{S}}\Vert }_{\infty }=\tau {\Vert {\widehat{\mathit{D}}}_{\mathit{S}}\Vert }_{\infty }/{\widehat{L}}^2$	$2\times {10}^{-4}-0.2$
${\Vert {\mathit{D}}_{\mathit{B}}\Vert }_{\infty }\sim {\Vert {\mathit{D}}_{\mathit{S}}\Vert }_{\infty }$	$2\times {10}^{-4}-0.2$
$\eta =\tau \widehat{\eta }/\widehat{L}$	Unknown