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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 39 "Phase Portrait Three Di
mensional System" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart
:\nwith(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Define the differential equatio
n using parameters:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a :=
 0.1; b := 0.1; c := 14;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
136 "RosslerDE := [diff(x(t),t) = -y(t) - z(t),\n              diff(y(
t),t) = x(t) + a*y(t),\n              diff(z(t),t) = b + z(t)*(x(t) -c
)];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "The initial conditions are
 given in the first line and can be changed." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 57 "IC:=[[x(0)= 5,y(0)=0, z(0)=0],[x(0)= 16,y(0)=0, \+
z(0)=0]];" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Plot x versu
s z" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "DEplot(RosslerDE, [
x(t),y(t),z(t)], t=0..50,  \n  IC,linecolour=BLUE, x=-30..30, y=-30..3
0,z=-1..40, stepsize=0.01,\n  arrows=NONE, method=classical[rk4],scene
=[x,z]);" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Plot \+
y versus z" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "DEplot(Rossl
erDE, [x(t),y(t),z(t)], t=0..50,  \n  IC,linecolour=BLUE, x=-30..30, y
=-30..30,z=-1..40, stepsize=0.01,\n  arrows=NONE, method=classical[rk4
],scene=[y,z]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Plot x versus \+
y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "DEplot(RosslerDE, [x(
t),y(t),z(t)], t=0..50,  \n  IC,linecolour=BLUE, x=-30..30, y=-30..30,
z=-1..40, stepsize=0.01,\n  arrows=NONE, method=classical[rk4],scene=[
x,y]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "3 Dimensional plot whic
h can be rotated:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 220 "IC3d:
=[[x(0)= 16,y(0)=0, z(0)=0]];\nDEplot3d(RosslerDE, [x(t),y(t),z(t)], t
=0..70,thickness=1,  \n  IC3d,linecolour=BLUE, x=-30..30, y=-30..30,z=
0..45, \n  stepsize=0.01,\n  arrows=NONE, method=classical[rk4],scene=
[x,y,z]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Plot t versus x" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 214 "ICt:=[[x(0)= 16,y(0)=0, z(0
)=0]];\nDEplot(RosslerDE, [x(t),y(t),z(t)], t=0..100,  \n  ICt,linecol
our=BLUE,thickness=1, x=-30..30, y=-30..30,z=0..50,   stepsize=0.01,\n
  arrows=NONE, method=classical[rk4],scene=[t,x]);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG }{EXCHG }{EXCHG }}{MARK "1 0 0" 
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