7a272778-0c8f-4bbc-81c4-c9ebbc59d84e 7 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

2 f 2 g x.0 NumIter dt dynSys ξ x.0 : x ξ : k 1 NumIter range ξ ξ dt ξ ξ r g f * + eval : x x ξ augment : 21 line for x 41 line :

EXAMPLE 3 - Nonlinear Equations (Lorentz Model)

x u Lorentz 5 x 2 el x 1 el - (* x 1 el x 3 el * - 15 x 1 el * + x 2 el - x 1 el x 2 el * 1 x 3 el * - 31 mat :

x r Ctrl 0 :

NOT all x0 can be '0' x0 0 0.1 013 mat transpose :

0.1 0.2 0.3 13 mat

Sol4 x u Lorentz x r Ctrl x0 500 0.02 dynSys :

Sol4 0 0.01 0.0188 0.0268 0.0344 0.0418 0.0493 0.1 0.098 0.099 0.1027 0.1087 0.1168 0.1271 00 1.96 105 -^* 5.6447 105 -^* 0.0001 0.0002 0.0003 37 mat

x1 Sol4 1 row transpose :

x2 Sol4 2 row transpose :

x3 Sol4 3 row transpose :

x3 x2 augment x3 x1 augment x2 x1 augment 3 1 sys Sol4 transpose

Lorentz attractor Rkadapt project

u Y D 8 Y 1 el * - 8 Y 2 el * + 30 Y 1 el * Y 1 el + Y 1 el Y 3 el * - Y 1 el Y 2 el * 83 / Y 3 el * - 31 mat :

t0 0 : t1 10 : N 2000 : 31 line

init 1 - 0131 mat :

s init t0 t1 N u Y D Rkadapt : y0 s 1 col s 2 col augment : y1 s 1 col s 3 col augment : y2 s 1 col s 4 col augment : 41 line

Lorentz triplet solutions

y0 y1 y2 3 1 sys

Compose as you wish, play/zoom/rotate Lorentz3D s 1 col s 2 col s 3 col augment :

s 2 col s 3 col augment Lorentz3D