Fig. 3.

Non-trivial dependency of Turing instabilities on geometric parameters. Plots of $max(\mathfrak{R}(\lambda ))$ given by Eq. (28) in blue computed across 250 values of $\eta$ for different parameter combinations, and plots of $F_h(u_S)$ given by (46) in red asterisks for 100 values of $\eta$. The other parameters were taken as $a=0.1$, $b=2$, $d_u={10}^{-3}$, $d_v={10}^{-1}$, $\tilde{L}=1$. The constant c in $F_h$ was fixed per set of parameters/panel to match the maxima of $max(\mathfrak{R}(\lambda ))$ and $F_h$ across $\eta$ to qualitatively compare these metrics. The parameter sets corresponding to $h={10}^{-1},\epsilon ={10}^{-1}$ and $h=1,\epsilon ={10}^{-1}$ gave qualitatively the same results as in panel (c) with $max(\mathfrak{R}(\lambda ))>0$ for all $\eta$ (Color figure online)