Lotka Volterra Calculator
Calculate lotka volterra with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
dN/dt = alpha*N - beta*N*P | dP/dt = gamma*N*P - delta*P
Prey equation: exponential growth reduced by predation. Predator equation: growth from consumption minus mortality. Equilibrium at N*=delta/gamma, P*=alpha/beta. Period approximately 2pi/sqrt(alpha x delta).
Worked Examples
Example 1: Classic Predator-Prey
Problem:100 prey, 20 predators. alpha=0.5, beta=0.01, delta=0.3, gamma=0.005. Simulate 100 time units.
Solution:Prey equilibrium = delta/gamma = 0.3/0.005 = 60\nPredator eq = alpha/beta = 0.5/0.01 = 50\nPeriod = 2pi/sqrt(0.5 x 0.3) = 16.23\nStarting above prey eq, below pred eq\nPrey initially decline as predators increase
Result:Equilibrium: Prey=60, Pred=50 | Period=16.23
Example 2: High Efficiency Predator
Problem:100 prey, 10 predators. alpha=0.8, beta=0.02, delta=0.4, gamma=0.01.
Solution:Prey eq = 0.4/0.01 = 40\nPred eq = 0.8/0.02 = 40\nPeriod = 2pi/sqrt(0.8x0.4) = 11.11\nHigher conversion produces faster response
Result:Equilibrium: Prey=40, Pred=40 | Period=11.11
Frequently Asked Questions
What are the Lotka-Volterra equations?
The Lotka-Volterra equations are paired first-order nonlinear differential equations describing predator-prey dynamics. Independently derived by Lotka in 1925 and Volterra in 1926, they model prey growing exponentially without predators and declining proportionally to predator encounters. Predator populations grow from prey consumption and decline at natural mortality rate. The system produces characteristic oscillating population cycles where predator peaks lag prey peaks. Despite simplicity, they capture the fundamental feedback mechanism observed in many natural systems.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy