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Lotka-Volterra Model

Lotka-Volterra Model
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2016-08-25 11:35
FunctionCalculusInequalitySlider AnimationGraphing
This example demonstrates the periodic population dynamics of predator-prey systems through graphical representations. Core math concepts include differential equations, function graphing, and continuity. Construction highlights involve commands like SolveODE, Length, First, Sequence, Element, Distance, Textfield, Ray, Text, NSolveODE, Point, Last, If, Segment, Polygon, Centroid in GeoGebra. Suitable for high school students and users interested in ecological mathematical models.

GeoGebra Commands & Parameters

  1. SolveODE(g, f, x(A), y(A), time, step) → numericalIntegral1
  2. Length(numericalIntegral1) → len01
  3. First(numericalIntegral1, len01) → list1
  4. Sequence((floor((step * i)), x(Element[list1, i])), i, 1, len01) → listprey
  5. Element(listprey, explore) → preyPoint
  6. Sequence((floor((step * i)), y(Element[list1, i])), i, 1, len01) → listpredator
  7. Element(listpredator, explore) → predPoint
  8. Element(list1, position) → B
  9. Distance(B, P2) → Cond
  10. Textfield(x_0) → InputBox1
  11. Textfield(y_0) → InputBox2
  12. Textfield(h) → InputBox3
  13. Ray(timePoint, predPoint) → i
  14. Text(("Pred=" * y(predPoint))) → textprey
  15. Text(("Prey=" * y(preyPoint))) → textpred
  16. NSolveODE({f1, g1}, 0, {x_0, y_0}, time) → numericalIntegral2, numericalIntegral2_2
  17. Point(numericalIntegral1) → C
  18. Last(listpredator) → Lastpredator
  19. Element(Lastpredator, 1) → MM
  20. If(MM ≟ MM, MM, (1 / 2, 1 / 2)) → MMM
  21. Segment(D, C') → k
  22. Segment(E, C') → j
  23. Polygon(F, G, 5) → poly1, l, m, n, p, q, H, I, J
  24. Centroid(poly1) → K