# Ecology: Lotka–Volterra The classic predator–prey oscillator. **Prey grow on their own, predators decline without food, and chance encounters couple the two populations** into the canonical boom-bust cycle. ## What it simulates - Prey reproduce when predators are scarce. - Predator–prey encounters reduce prey and feed predator reproduction. - Predators decline without prey. - The system circles a non-zero equilibrium at `N* = gamma/delta`, `P* = alpha/beta`. - An invariant-drift audit checks that the numerical integrator is faithful to the conserved quantity.  ## Run it on the Hub 1. Open the [Lotka–Volterra System Lab](https://hub.biosimulant.com/labs/52e99dd4-17c7-47a5-b8bc-e59319d71b25) on the public Hub. 2. Click **Run**. The default scenario runs for 250 days. ## Inputs you can tune | Input | Meaning | |---|---| | `prey_initial_population` | Starting prey count. | | `predator_initial_population` | Starting predator count. | | `prey_growth_rate` | Prey growth in the absence of predators. | | `predation_rate` | How strongly predator–prey encounters reduce prey. | | `predator_mortality_rate` | Predator decline without prey. | | `predator_reproduction_rate` | How prey encounters add to predators. | ## What results to expect - **Population trajectory**: lagged predator–prey oscillations. - **Phase portrait**: a closed loop around the non-zero equilibrium, with start/end markers and the `dN/dt = 0` and `dP/dt = 0` nullclines. - **Summary table**: parameters, equilibrium, final populations, min/max ranges, and an estimated cycle period. - **Invariant-drift audit**: a numerical-quality check; large drift means the integration step is too coarse.  **Info:** Source on GitHub: [models-ecology — lotka-volterra-system](https://github.com/Biosimulant/models-ecology/tree/main/labs/ecology-lotka-volterra-system). For carrying capacity, seasons, disease, or migration, use the Rosenzweig–MacArthur lab instead.