Each node i is a startup, corporation, or research institution with a knowledge stock Ki and capital Ci. Every actor type has its own base R&D rate ri (startups highest, corporations lowest, research institutions fixed) and capital multiplies it:
dK_i/dt = r_i · C_i + σ · Σ_j∈N(i) w_ij (K_j − K_i)
The first term is internal R&D output funded by capital; the second is diffusion — knowledge spills from well-connected neighbours toward node i at rate σ (the spillover slider), exactly like heat conduction across a graph. Links between nodes form and dissolve stochastically each tick with probability proportional to the collaboration-propensity slider p, weighted by a type-compatibility matrix (research↔startup links spill fastest, corp↔corp links slowest).
An innovation event fires for node i as a Poisson process with instantaneous rate λi = k·Ki² — innovation output grows super-linearly with accumulated knowledge, so well-connected, well-funded hubs innovate disproportionately more often (a cumulative-advantage effect seen in real R&D networks). Each event resets that node's knowledge partway and emits a visible burst.
- Startup funding — scales capital for orange startup nodes only, showing how funding concentration shifts where innovation clusters.
- Collaboration propensity — the per-tick probability any two compatible nodes form a new link.
- Spillover rate σ — how fast knowledge equalises across an existing link.