Predator–Prey Simulator
The Lotka–Volterra model describes two interacting species — prey that breed on their own and predators that survive only by eating the prey. Four rates govern it: prey growth α, predation β, predator growth from eating δ and predator death γ. Set those and the starting populations and the simulator integrates the coupled equations with fourth-order Runge–Kutta, drawing two things at once: a time series of both populations rising and falling out of phase, and a phase-plane plot where the state traces a closed orbit around the coexistence equilibrium. The equilibrium point (γ/δ prey, α/β predators) is marked so you can see the orbit circle it.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Update rules: prey change dx/dt = αx − βxy, predators dy/dt = δxy − γy. Predators grow only in proportion to how often they meet prey.
- The equilibrium sits at x* = γ/δ prey and y* = α/β predators; any other start orbits around it forever without settling — the cycles never damp out.
- Predator peaks lag prey peaks by a quarter cycle: prey crash first, then predators starve and crash after them.
- Runs 100% in your browser — simulations are computed locally on your device.
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