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罗斯勒吸引子

罗斯勒吸引子
几何画板及绘图内容加载中，请稍等……
2017-08-30 09:14
函数三角函数立体几何微积分参数方程
所属专题 UQ-Applied Mathematical Analysis
①本范例演示了罗斯勒吸引子这一混沌系统的分形轨迹；②涉及的核心数学概念包括微分方程、混沌理论、参数方程、三维空间可视化；③作图要点提炼自构造摘要，用到了对象（如按钮、滑块）和命令（如t, A, k1, j1, i1等参数控制）来动态展示吸引子的形态变化；④适合高中及以上学生及对混沌动力学感兴趣的数学爱好者学习探索。

GeoGebra 命令及参数

  1. Numeric strength(2)
  2. Numeric n(12)
  3. Numeric h(0.01)
  4. Numeric speed(1)
  5. Numeric t(4.27)
  6. Numeric b(0.2)
  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. {(-2.4935544514881176, 12.775080288013005, -5.20662587161766), (-7.029664706191961, -12.484135647771105, 9.486399252792186), (-9.292163411414823, -5.5481637786395765, 26.483372718501247), (13.86231517
  14. {-2.677424871442329, -28.948279540725736, -4.83982238476226, -13.060903063494495, 12.59787727608522, -9.492541520355994, -22.36316466013438, 20.402677772818112, -10.02387759829951, 3.7397096976262674,
  15. {-5.153372142875115, 8.498505151968477, -12.94931822901259, 7.669800348233621, 1.852319455519483, -6.384409879286964, 34.30972242709876, -4.629909374695141, -12.376827682886447, -28.22161414457551, -1
  16. {-0.010731304150261023, -19.063614299995947, -25.48084505354133, -24.579554121473272, 0.09835451152242808, -0.023354837604977224, -50.30364083653461, -18.664143155926553, -12.045315765564851, -2.45403
  17. {-2.625783836972076, -28.84262844924546, -4.455520751936721, -12.891805525762097, 12.5783705364148, -9.428463873187075, -22.20322547604002, 20.635618298124328, -9.779656163814996, 4.046466155478011, 2
  18. {-5.190453135875289, 8.226019366865156, -13.023615089318238, 7.554530918295143, 1.9820028671913743, -6.4921041142490985, 34.15471022535162, -4.43514241571635, -12.501820114235215, -28.240660275888402,
  19. {-0.01045733755596373, -24.49527632541202, -22.35241752625538, -25.09498619770222, 0.100388966476681, -0.023088920715954975, -53.93228071704132, -17.286147517811685, -10.54701370603463, -1.97511731277
  20. {-2.625415766708017, -28.785586971140265, -4.486062058606524, -12.885498510700424, 12.57705335774854, -9.427389590006344, -22.165388955217484, 20.619890672153392, -9.793389260096811, 4.041867473512927
  21. {-5.1900108875165865, 8.226530906209753, -13.019920666710595, 7.55599135481259, 1.9820671666180134, -6.491678726247333, 34.15599959278907, -4.43242347654533, -12.499627884753068, -28.23763080357251, -
  22. {-0.010468378004341583, -24.43972485081798, -22.739123437304997, -25.07370262089858, 0.10031044048114562, -0.023101491232946553, -54.2465436809246, -17.35867388826886, -10.738391188339467, -2.06784808
  23. {-2.573415286131911, -28.62401566183357, -4.124641502681948, -12.710548838172773, 12.556229723943238, -9.362245916006389, -21.96135377837167, 20.838499720114395, -9.55911721683766, 4.345819275484593,
  24. {-5.226640501759342, 7.955699536170511, -13.091119152851563, 7.442314343438862, 2.111788791340926, -6.598924385992081, 34.003038646365574, -4.235241255158255, -12.622693979627396, -28.253727318319545,
  25. {-0.010200638304565635, -29.724451759316906, -19.891298237335334, -25.53539483530637, 0.10239679036684513, -0.022823421320407544, -58.12518580241106, -16.081476495650836, -9.371913926274585, -1.646523
  26. Numeric a(0.2)
  27. Numeric c(5.7)
  28. F(x, y, z) = (strength * ((-y) - z))
  29. G(x, y, z) = (strength * (x + (a * y)))
  30. H(x, y, z) = (strength * (b + (x * z) - (c * z)))