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Lotka-Volterra 模型

Lotka-Volterra 模型
几何画板及绘图内容加载中，请稍等……
2016-08-25 11:35
函数微积分不等式滑块动画函数图像
①本范例演示了捕食者-被捕食者动态系统的周期性种群数量变化图形；②涉及的核心数学概念为微分方程、函数图像、连续性；③作图要点：使用了 SolveODE, Length, First, Sequence, Element, Distance, Textfield, Ray, Text, NSolveODE, Point, Last, If, Segment, Polygon, Centroid 等GeoGebra命令与对象；④适合高中及以上学生及需要理解生态数学模型的用户。

GeoGebra 命令及参数

  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