Predator–Prey (Lotka–Volterra)
Cyclical population dynamics.
Key idea
Cyclical population dynamics.
In depth
x′ = ax − bxy (prey), y′ = −cy + dxy (predators). Populations oscillate in closed cycles around an equilibrium with predators lagging prey. It showed how interacting species can cycle without outside forces.
Worked example
With a = 1, b = 0.1, c = 1.5, d = 0.075, equilibrium at (20, 10).
Formula
Real-world uses
- Understanding lynx and hare population cycles and fishery management
Common mistake
Expecting the model to include limits on growth; the basic version has none.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Predator–Prey (Lotka–Volterra)?
Cyclical population dynamics. It is a topic at the expert level in Differential Equations, Abstract Algebra & Applied Math.
What is the formula for Predator–Prey (Lotka–Volterra)?
The key formula is x′ = ax − bxy, y′ = −cy + dxy.
Where is Predator–Prey (Lotka–Volterra) used in real life?
Real-world examples: Understanding lynx and hare population cycles and fishery management.
What should I learn before Predator–Prey (Lotka–Volterra)?
Make sure you are comfortable with Equilibria and Stability, the previous topic in Differential Equations, Abstract Algebra & Applied Math.
What is a common mistake with Predator–Prey (Lotka–Volterra)?
Expecting the model to include limits on growth; the basic version has none.
How can I practise Predator–Prey (Lotka–Volterra)?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Predator–Prey (Lotka–Volterra)?
Move on to SIR Epidemic Model next.
Related expert topics in Differential Equations, Abstract Algebra & Applied Math
- Exact Equations – M dx + N dy = 0 with Mᵧ = Nₓ.
- Bernoulli Equations – Substitute v = y¹⁻ⁿ to linearise.
- Runge–Kutta Methods – Higher-accuracy numerical solvers.
- Second-Order Homogeneous Equations – Use the characteristic equation.
- Undetermined Coefficients – Guess the particular solution form.
- Variation of Parameters – General method for particular solutions.