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Lotka-Volterra Predator-Prey Model

Lotka-Volterra Predator-Prey Model
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2016-08-10 15:37
VectorFunctionCalculusDerivativeGraphing
This example demonstrates the dynamic behavior and phase plane of the Lotka-Volterra predator-prey model. Key mathematical concepts include differential equations, population dynamics, oscillatory behavior, derivatives, and integrals. GeoGebra commands used in construction include SolveODE (solving differential equations), Length (calculating length), First (getting the first element of a list), Sequence (generating a sequence), Max (finding the maximum value), PolyLine (creating a polyline), Polygon (creating a polygon), Vector (creating a vector), Element (accessing an element), Textfield (creating a text field), and Segment (creating a segment). Suitable for high school students and learners interested in population dynamics models.

GeoGebra Commands & Parameters

  1. SolveODE(DY, DX, x(A), y(A), t, step) → solutionde
  2. Length(solutionde) → points
  3. First(solutionde, points) → solutionpoints
  4. Sequence(x(Element[solutionpoints, i]), i, 1, N) → list1
  5. Sequence(y(Element[solutionpoints, i]), i, 1, N) → list2
  6. Max(list1) → maximum1
  7. Max(list2) → maximum2
  8. Sequence(((2 * i / N), Element[list1, i] / maximum22 + 1.5), i, 1, N) → list3
  9. Sequence(((2 * i / N), Element[list2, i] / maximum22 + 1.5), i, 1, N) → list4
  10. PolyLine(list3) → Prey
  11. PolyLine(list4) → Predator
  12. Polygon(C, D, F, E) → poly1, c_1, d_1, f, e
  13. Vector(G, I) → u
  14. Vector(G, H) → v
  15. Element(solutionpoints, N) → J
  16. Textfield(x_0) → InputBox1
  17. Textfield(y_0) → InputBox2
  18. Segment(K, J) → g
  19. Segment(L, J) → h
  20. SolveODE(DY, DX, x(A), y(A), tiempos - step, step) → sol02