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洛伦兹吸引子 by Juan Carlos Ponce Campuzano

洛伦兹吸引子 by Juan Carlos Ponce Campuzano
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2017-08-31 05:47
向量微积分最值优化参数方程函数图像
所属专题 UQ-Applied Mathematical Analysis
①本范例演示了洛伦兹吸引子这一混沌系统的三维轨迹图形；②涉及的核心数学概念包括微分方程、动力系统、混沌理论；③作图要点提炼自构造摘要，使用了对象如按钮(button1, button2等)、滑块(strength, n等)、参数(t, A等)以及GeoGebra命令如rotate, F, G, H等；④适合高中及以上学生及对混沌理论感兴趣的数学爱好者学习研究。

GeoGebra 命令及参数

  1. Numeric strength(1)
  2. Numeric n(12)
  3. Numeric h(0.005)
  4. Numeric speed(1)
  5. Numeric t(-4.87)
  6. Numeric b(28)
  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. {(2.5900232040706044, -11.745281970900995, 11.972308465297743), (-17.699184163363643, -6.357120819982558, 5.306662403559168), (-1.7864398197719638, -14.15989079075698, 29.822708899574547), (4.04569321
  14. {-52.576231401426874, -142.49284271042933, -54.25953403929643, 1.11298387575129, -71.95894395262525, -28.49168309426335, -100.1769946728455, -35.70029739931038, -10.801192523512988, -65.0535852731946,
  15. {-159.95423433259026, 174.47382359061828, -29.337511818739273, 5.240248472407367, 36.63912375843727, -40.180983591025516, -8.47105035270892, 9.454213657658478, -37.5550033644864, -100.15438068888069,
  16. {45.54589040925377, -43.505557292695755, -63.123531028357675, -18.13182095463214, 101.58696070574612, 2.406689799407336, -42.01374165301707, -51.85485589200321, 57.91105660672137, -12.300796977606986,
  17. {-55.26068147470596, -134.56867605290313, -53.6364834837825, 1.2161654906676915, -69.2439922598487, -28.78391560668241, -97.88434606484209, -34.57143462288615, -11.470037794537316, -65.93110515858675,
  18. {-159.72074080958487, 163.81250310766853, -27.69125093895355, 5.29335913582955, 39.40664069652789, -41.85399411629992, -7.125865565472509, 9.531164473655995, -39.050283442191784, -98.22479478276802, -
  19. {38.60683248990378, -37.92964386098798, -63.2915924019852, -18.0360598839176, 103.20631381416901, 2.91186254209466, -42.374965214239715, -51.471594056828515, 56.26941471253725, -15.953943600332714, 16
  20. {-55.18773288479885, -135.03331323141506, -53.6109032256757, 1.2149137168803366, -69.24267812871582, -28.818435057003793, -97.90803266036124, -34.59773242189682, -11.49069866470434, -65.86092751379913
  21. {-159.4072431507419, 164.36927325969378, -27.700350552453592, 5.298033903396321, 39.423644214881364, -41.86576194167846, -7.122186476175752, 9.537090884628084, -38.9954710169387, -98.10687230169428, -
  22. {38.59344291057549, -38.25966270947698, -63.26648988287549, -18.036389200845107, 103.0169771395164, 2.920581238975151, -42.32821167674902, -51.47469010808287, 56.2177633505402, -15.891000105563727, 16
  23. {-57.78720691472402, -127.52271338587389, -52.964006405635324, 1.3171398850770895, -66.52562783544538, -29.144049438497078, -95.63770236363624, -33.49355623398413, -12.176431141124713, -66.66588251258
  24. {-158.83823107522122, 154.13530207861027, -26.10687017286258, 5.3559519634571995, 42.28796020755482, -43.553671433056515, -5.827680862699681, 9.597309128348323, -40.424929308988226, -96.0794983941778,
  25. {31.775927109049604, -33.25417499088631, -63.391348658447974, -17.940869279456333, 104.41382223105145, 3.4503948680744765, -42.634385082653395, -51.09845303431716, 54.532656066820884, -19.392570285271
  26. Numeric a(10)
  27. Numeric c(2)
  28. (0, 0, 1)
  29. Boolean rotate(true)
  30. F(x, y, z) = (strength * (a * (y - x)))
  31. G(x, y, z) = (strength * ((x * (b - z)) - y))
  32. H(x, y, z) = (strength * ((x * y) - (c * z)))