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Rabinovich–Fabrikant 吸引子

Rabinovich–Fabrikant 吸引子
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2017-08-31 06:03
函数变换参数方程滑块动画
所属专题 UQ-Applied Mathematical Analysis
这个范例演示了 Rabinovich–Fabrikant 吸引子，这是一种混沌动力系统的典型例子。它涉及复杂的非线性动力学和混沌理论。通过调整参数，可以观察到系统的动态行为。该范例使用了 GeoGebra 的滑块动画功能，展示了系统的演化过程。适合高中及以上学生和教师使用。

GeoGebra 命令及参数

  1. Numeric strength(1.0)
  2. Numeric n(12.0)
  3. Numeric h(0.005)
  4. Numeric speed(1.0)
  5. Numeric t(-4.2)
  6. Numeric b(20.0)
  7. x(CornerThreeD[-1, 3])
  8. x(CornerThreeD[-1, 1])
  9. y(CornerThreeD[-1, 3])
  10. y(CornerThreeD[-1, 1])
  11. z(CornerThreeD[-1, 5])
  12. z(CornerThreeD[-1, 3])
  13. {(-2.6537232166142735, 1.8567837910561718, 2.4787129494073525), (4.52780306425937, 1.5435666672596504, -3.608198848553217), (-2.811757228001034, 4.321221598037576, 2.4568714899224027), (4.036983636939
  14. {-24.568645574594193, 1.3624953971181102, -2.6941070371664297, -1.9157432708647657, -5.938137220732006, 4.646513726802567, -210.983509097447, -3.156072108700701, 52.180437160474185, -17.13360152018484
  15. {4.987198969898754, -8.488851183403925, -6.943545925561837, -0.19941956533671368, 51.29549906803594, 10.320624385556266, 21.06530558405817, 2.2415823071196175, -12.78289962414873, 28.447087194267795,
  16. {43.17466413517023, 2.274612840735854, -7.970595073150294, 3.1519100534236784, -2.1615740701124304, 1.3800013284403898, -507.7638020093168, 0.9931377056103823, 110.0327364242936, 39.96322298304967, -4
  17. {-23.93164111258039, 1.3553638189742436, -2.7315890772045064, -1.9122846981164676, -3.9766907467935857, 4.719433564446149, -235.96423369673894, -3.1391551903499275, 49.88971332194121, -14.869550819151
  18. {5.738736421313698, -8.515284330690852, -6.920364183292033, -0.17090407921812512, 52.13567088739895, 10.139916600573255, 82.54056964554276, 2.197016799802602, -15.49207508063271, 31.4577142379225, 3.6
  19. {43.280954797565826, 2.180669547198492, -7.986826879746822, 3.164826596527627, -1.5152376594583172, 1.4258331237135164, -462.9303231473703, 0.8976852473174249, 110.1602445368585, 33.893816785623734, -
  20. {-23.95170004023457, 1.3553573011372368, -2.7316845708438615, -1.9123503133578934, -3.938648843273822, 4.716274717922903, -234.29107307902032, -3.1388538498451206, 49.97855932174467, -14.6671066251703
  21. {5.739372836629293, -8.516292557305373, -6.920523393672667, -0.17073755664457968, 51.898217032084105, 10.135917756537376, 86.0973535851391, 2.196804715361699, -15.480555669757585, 31.051677762587445,
  22. {43.3087651837096, 2.180843314446795, -7.986741532596695, 3.16487512642291, -1.508673790435696, 1.4254160276869143, -462.6345293684906, 0.8983138097882571, 110.30517241189287, 33.2727662194104, -4.199
  23. {-23.372806606455196, 1.3475167003096096, -2.769154235839829, -1.9090821552195396, -1.9379712843010475, 4.783702918602666, -257.4470448708041, -3.1220034134994163, 47.969347620503086, -12.304830269149
  24. {6.413418520530221, -8.543734044062942, -6.896390882328101, -0.14243453531341954, 52.493530864902496, 9.95370309823603, 166.88662921759502, 2.1517277845825253, -17.75035701007757, 33.51957221172797, 3
  25. {43.31028247947829, 2.087462958987278, -8.001902958102342, 3.1774197610976223, -0.8663313039535422, 1.471041067473638, -403.471269174632, 0.803708388724774, 109.78852262443236, 26.728634952505352, -4.
  26. Numeric a(10.0)
  27. Numeric c(2.6666666666666665)
  28. (0, 0, 1)
  29. Boolean rotate(true)
  30. Numeric alpha(1.1)
  31. Numeric gam(0.87)
  32. F(x, y, z) = (strength * ((y * (z - 1 + (x * x))) + (gam * x)))
  33. G(x, y, z) = (strength * ((x * ((3 * z) + 1 - (x * x))) + (gam * y)))
  34. H(x, y, z) = (strength * ((-2 * z) * (alpha + (x * y))))