MathPlotAI Logo MathPlotAI

Lotka-Volterra Predator-Prey Model by Juan Carlos Ponce Campuzano

Lotka-Volterra Predator-Prey Model by Juan Carlos Ponce Campuzano
Loading the math board and drawing, please wait…
2016-08-08 18:28
FunctionCoordinate GeometryCalculus
In collections UQ-Applied Mathematical Analysis
This example demonstrates the interaction between two species in a predator-prey relationship. Key mathematical concepts include differential equations and coordinate geometry. Using GeoGebra commands like SolveODE, Vector, and Intersect, the model dynamically shows the changes in predator and prey populations over time. Suitable for high school and above students studying population dynamics.

GeoGebra Commands & Parameters

  1. SolveODE(G, F, x(B), y(B), t, step) → solutioneq
  2. Length(solutioneq) → npoints
  3. First(solutioneq, npoints) → list0
  4. Sequence(x(Element[list0, i]), i, 1, npoints) → list1
  5. Sequence(y(Element[list0, i]), i, 1, npoints) → list2
  6. Max(list1) → e
  7. Max(list2) → g
  8. Sequence(((4 * i / N), (2 * Element[list1, i] / f)), i, 1, N) → list3
  9. Sequence(((4 * i / N), (2 * Element[list2, i] / h) + 3), i, 1, N) → list4
  10. Vector(C, E) → u
  11. Vector(C, D) → v
  12. Sequence(Sequence[Vector[((10 * j / f), (10 * k / h)), ((10 * (j + (scale * F(j, k))) / f), (10 * (k + (scale * G(j, k))) / h))], j, 0, xmax, xstep], k, 0, ymax, ystep) → list5
  13. Intersect(xAxis, yAxis) → I
  14. Point(xAxis) → J
  15. Point(yAxis) → K
  16. Point(yAxis) → L
  17. Point(yAxis) → M
  18. Vector(I, J) → w
  19. Vector(I, K) → i
  20. Vector(L, M) → j
  21. Vector(L, O) → k
  22. PolyLine(list3) → l
  23. PolyLine(list4) → m
  24. Sequence(((10 * Element[list1, i] / f), (10 * Element[list2, i] / h)), i, 1, N) → list6
  25. Segment(T, B') → n
  26. Segment(S, B') → p
  27. Segment(R, P) → q
  28. Segment(P, Q) → r
  29. Textfield(a) → InputBox1
  30. Textfield(b) → InputBox2
  31. Textfield(c) → InputBox3
  32. Textfield(d) → InputBox4
  33. Textfield(A_0) → InputBox5
  34. Textfield(B_0) → InputBox6

AI Drawing Prompt Reference

Create a predator-prey model diagram in a coordinate plane with four parameter input boxes and two initial-population input boxes. Plot two time-series polylines derived from the differential-equation solution, one for prey and one for predator, scaled to the axes. Add a vector-field grid in the phase plane whose arrows are determined by the model equations, showing population change directions. Include points on the axes, several vectors anchored to those points, and line segments connecting related points to illustrate the dynamic relationship.
The prompt above was compiled from the original drawing commands and is for reference only.