Lotka-Volterra — Predator-Prey Population Dynamics

🐇🦊 Lotka-Volterra Model

The Lotka-Volterra equations describe cyclic oscillations between predator and prey populations. Prey grow logistically; predators grow by consuming prey. The system produces perpetual cycles — a fundamental result in theoretical ecology.

🎛 Parameters

Prey growth rate r 1.0 Predation rate α 0.10 Predator efficiency β 0.075 Predator death rate m 0.50 Initial prey H₀ 10 Initial predators P₀ 5

🔭 View

📐 Equilibrium

Prey eq. H*

6.7

Predator eq. P*

10.0

Cycle period (yr)

6.3

Max prey / pred

—

ℹ️ Equations

dH/dt = r·H − α·H·P
Prey grow at rate r; eaten at rate α per predator.

dP/dt = β·α·H·P − m·P
Predators grow by eating prey (efficiency β); die at rate m.

Equilibrium: H* = m/(β·α), P* = r/α — a center (neutral stability), orbits closed.