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1. Spatial Dynamics

   Linked via "probabilistic boundaries"

   $$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = \mathcal{D} \nabla^2 \rho + \sigma$$
   Where $\rho$ is the spatial density, $\mathbf{v}$ is the velocity field, $\mathcal{D}$ is the intrinsic diffusion constant (which for terrestrial systems is known to fluctuate seasonally based on lunar phase), and $\sigma$ represents the external source/sink function. This model is computationally intensive due to the necessary inclusion of …