Fig. 10

Spatial distribution of population density under varying toxin fields and activation sensitivities. Columns represent different activation functions’ analytical solution, \(\tanh (\textrm{y}_1)\), \(\tanh (2\textrm{y}_1)\), and \(\tanh (10\textrm{y}_1),\) while rows correspond to different toxin configurations. The color intensity indicates population density, with higher values representing stronger survival. This visualization supports the observation that \(\tanh (2\textrm{y}_1)\) yields more consistent performance across toxin environments.