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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 35 "Phase Portrait for a Li
enard System" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart:\nw
ith(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Define the differential equation a
nd parameters:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "LorenzDE
 := [diff(x(t),t) = sigma*(y(t)-x(t)),\n             diff(y(t),t) = r*
x(t)-y(t) -x(t)*z(t),\n             diff(z(t),t) = x(t)*y(t) -b*z(t)];
\nsigma := 10; b := 8/3; r := 28;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
70 "The initial conditions are given in the first line and can be chan
ged." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "IC:=[[x(0)= 0.1,y(0
)=0.1, z(0)=0],[x(0)= -0.1,y(0)=-0.1, z(0)=0]];" }}}{EXCHG }{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 15 "Plot x versus z" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 208 "DEplot(LorenzDE, [x(t),y(t),z(t)], t=0..20,  \n
  IC,linecolour=BLUE, x=-30..30, y=-30..30,z=0..50, stepsize=0.01,\n  \+
arrows=NONE,thickness=1, method=classical[rk4],scene=[x,z], \n  title=
`Lorenz System: (x,z)`);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "3 Dim
ensional plot which can be rotated:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 202 "DEplot3d(LorenzDE, [x(t),y(t),z(t)], t=0..20,  \n  I
C,linecolour=BLUE, x=-30..30, y=-30..30,z=0..50, stepsize=0.01,\n  arr
ows=NONE, method=classical[rk4],scene=[x,y,z], \n  title=`Lorenz Syste
m: (x,y,z)`);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Plot t versus x
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 248 "ICt:=[[x(0)= 0.1,y(0)=
0.1, z(0)=0]];\nDEplot(LorenzDE, [x(t),y(t),z(t)], t=0..20,  \n  ICt,l
inecolour=BLUE,thickness=1, x=-30..30, y=-30..30,z=0..50,   stepsize=0
.01,\n  arrows=NONE, method=classical[rk4],scene=[t,x], \n  title=`Lor
enz System: (t,x)`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
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