models/henon.lua

   1 --%  ft| TRAJECTORY_T0_V0_A1_O0 sn| Chaotic~Hénon~attractor n| #0 d| 0.5 n| #1 d| 1 n| #2 d| 1.42 n| #3 d| 0.3 n| #4 d| 1000 n| #5 d| 10000 n| #6 d| 1000 n| #7 d| x n| #8 d| y
   2 --%  ft| BIFURCATION_1 sn| Period-doubling~route~to~chaos n| #0 d| 0.5 n| #1 d| 1 n| #2 d| 0.3 n| #3 d| a n| #4 d| 0.3 n| #5 d| 1.45 n| #6 d| -2 n| #7 d| 2 n| #8 d| 500 n| #9 d| 200 n| #10 d| x
   3 --@@
   4
   5 name = "Hénon"
   6 description = "See Model refs in user's guide"
   7 type = "D"
   8 parameters = {"a", "b"}
   9 variables = {"x", "y"}
  10
  11
  12 function f(a, b, x, y)
  13
  14     x1 = a - x^2 + b * y
  15     y1 = x
  16
  17     return x1, y1
  18
  19 end
  20
  21
  22 function Jf(a, b, x, y)
  23
  24         return
  25
  26         -2 * x, b,
  27         1,              0
  28
  29 end
  30
  31 -- inverse
  32 function g(a, b, x, y)
  33
  34     x1 = y
  35     y1 = (x - a + y^2) / b
  36
  37     return x1, y1
  38
  39 end
  40
  41
  42
  43