May's Stability Limit — Random Food Web Simulator

A generalized Lotka-Volterra model extends the classic two-species predator-prey equations to an entire community: every species gets its own growth rate, its own self-limiting crowding term, and a web of random interactions with the rest of the community. This simulator builds exactly that — a random community matrix with tunable species count S, connectance C (the fraction of possible links that exist) and interaction strength σ — then integrates the real ODEs live so you can watch the population of every species rise, fall or crash. Robert May's 1972 complexity-stability criterion, σ√(SC) < d, predicts from the matrix alone whether the web should settle into a stable equilibrium or spiral into extinction cascades, and the live simulation lets you test that prediction against the actual dynamics in real time.