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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 31 "Simulation of the Loren
z System" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
50 "Restart Maple and load the linear algebra package." }}{PARA 0 "" 
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:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}
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fine r.h.s. of equations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "f:=sigma*(y(t)-x(t)):g:=r*x(t)-y(t)
-x(t)*z(t):h:=x(t)*y(t)-b*z(t):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 21 "Set parameter values." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sigma:
=10:b:=8/3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r:=24.1:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "De
fine differential equations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "de1:=diff(x(t),t)=f:de2:=dif
f(y(t),t)=g:de3:=diff(z(t),t)=h:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "Define initial conditions." }}
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0 28 "ics:=[[0,1,1,1],[0,7,7,22]]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 91 "Obtain phase plot. In this case
 we have co-existence of strange attractor and stable focus." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "D
Eplot3d([de1,de2,de3],[x(t),y(t),z(t)],t=0..150,ics,stepsize=0.01,line
colour=blue);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "r:=22:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "de1:=diff(x(t),t)=f:de2:=dif
f(y(t),t)=g:de3:=diff(z(t),t)=h:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "Define initial conditions." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "ics:=[[0,5,5,7.5]]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 57 "Obtain phase plot. In this case we have t
ransient chaos.." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
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{MPLTEXT 1 0 6 "r:=40:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "d
e1:=diff(x(t),t)=f:de2:=diff(y(t),t)=g:de3:=diff(z(t),t)=h:" }}}
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lot time series to show sensitive dependence on initial conditions." }
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0 114 "DEplot([de1,de2,de3],[x(t),y(t),z(t)],t=140..145,ics,stepsize=0
.01,linecolour=[blue,green],scene=[t,x],maxfun=-1);" }}}}{MARK "26" 0 
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