Spatial Grid
Grass
Prey
Predator
Bare
Lotka-Volterra dynamics / Beinhocker Ch 8 p.168
The predator-prey system is one of the most fundamental examples of endogenous dynamics in complex systems. No external force drives the population cycles -- they arise purely from the internal logic of the interactions: prey reproduce, predators eat prey, predators starve when prey are scarce, prey rebound when predators decline.
Beinhocker uses Lotka-Volterra as a stepping stone toward the broader argument that economic systems are far-from-equilibrium -- they do not settle into a static optimum but continually oscillate, adapt, and restructure. The "invisible hand" is not a force toward equilibrium but a driver of perpetual motion through fitness landscapes.
The classic ODE model produces perfectly periodic orbits -- the system traces closed loops in phase space forever. But the agent-based spatial version introduces stochasticity, spatial heterogeneity, and the possibility of extinction. Small populations can vanish through random fluctuations even when the ODE predicts survival. This gap between the deterministic and stochastic views is central to Beinhocker's critique of traditional equilibrium economics.