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Lotka-Volterra Equations

  • Numerical solutions of Lotka–Volterra predator–prey model
  • Jul. 1, 2021 ~ Dec. 1, 2021
  • The Lotka-Volterra equations are a system of two first-order, nonlinear ODEs that describe the populations of predators and prey in a biological system. Over time, the populations of the predators and prey change according to the equations :

dx/dt = α x - β xy
dy/dt = δ xy - γ y

1. Classical prey-predator equations | Code

  • Population over time, Phase plot
  • Comparison of the solutions for all of the initial conditions

References

[1] Solve Predator-Prey Equations, https://kr.mathworks.com/help/matlab/math/numerical-integration-of-differential-equations.html?lang=en
[2] Solve System of ODEs with Multiple Initial Conditions, https://kr.mathworks.com/help/matlab/math/solve-system-of-odes-with-multiple-initial-conditions.html?lang=en