Lotka-Volterra Predator-Prey Population Dynamics — 3D Lab Simulation
Nonlinear differential model of ecological interaction generating periodic population cycles
Theoretical Foundation & Historical Context
Independently proposed by Alfred Lotka and Vito Volterra in the 1920s, this model mathematically explains the oscillating boom-and-bust cycles between predator and prey species.
Law: Lotka-Volterra Ecological Differential Equations | Scientist: Alfred J. Lotka & Vito Volterra | Year: 1925
Key Learning Objectives & Competencies
- ✓ Simulate interactive population cycles using Runge-Kutta numerical integration.
- ✓ Observe the conservation of the invariant first integral V(x, y) along trajectories.
- ✓ Evaluate how ecological harvesting and parameter variations alter cycle amplitude.
Mathematical Formulations & Differential Equations
\begin{cases} \frac{dx}{dt} = \alpha x - \beta x y \\ \frac{dy}{dt} = \delta x y - \gamma y \end{cases}
x represents prey population, y represents predator population
Physical Parameters & Units of Measurement
| Symbol | Physical Quantity | SI Unit | Default |
|---|---|---|---|
| alpha | Prey Growth Rate alpha | 1/tháng | 1.1 |
| beta | Predation Rate beta | — | 0.04 |
| gamma | Predator Mortality Rate gamma | 1/tháng | 0.4 |
| delta | Predator Efficiency delta | — | 0.02 |
Real-World & Industrial Engineering Applications
Marine fishery stock assessment and dynamic seasonal catch limits.
Biological control of invasive species in national park conservation.
Macroeconomic models of capital accumulation and wage labor cycles.
3-Step Controlled Experimental Protocol
- Step 1: Baseline Setup — Initialize the simulation in standard conditions and observe undisturbed system dynamics.
- Step 2: Parameter Variation — Gradually modulate physical parameters using the control panel sliders.
- Step 3: Verification & Phase Space Analysis — Compare phase space trajectories and conservation metrics against analytical ODE solutions.
Frequently Asked Questions (FAQ)
What is the Volterra Principle regarding pesticide application?
Vito Volterra proved that indiscriminately destroying both predators and prey in equal proportion actually increases the average prey population and decreases the predator population, often causing severe pest resurgence.
How does the model change if prey follow logistic growth instead of exponential?
Adding a carrying capacity term K transforms the closed neutral orbits into a stable spiral sink or a limit cycle, making the ecological model far more robust and realistic.
Can a predator-prey system exhibit deterministic chaos?
Two-species autonomous systems cannot exhibit chaos by the Poincaré-Bendixson theorem. However, introducing a third species (e.g., vegetation-herbivore-carnivore) or seasonal periodic forcing readily produces deterministic chaos.
Related Simulations & Experiments
Spatial molecular architecture and complementary base pairing
Self-regulating cyclic oscillations in predator-prey ecology
Compartmental transmission dynamics: Susceptible (S), Infectious (I), Recovered (R)
Interactive Simulation: Interactive real-time 60 FPS WebGL simulation is active in your browser. Rotate, zoom, and inspect physical apparatus components with full camera freedom.