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{SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "#Andrew Sommese \+
2004" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 125 "The original Lorenz e
quations (arising in the 1963 from weather)--strange attractors: the s
o called butterfly effect or chaos" }{TEXT 203 0 "" }}}{EXCHG {PARA 
200 "> " 0 "" {MPLTEXT 1 202 21 "deq1  := diff(x(t),t)" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 24 "\n       =7*(y(t)-x(t)) ;" }{MPLTEXT 1 
202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I%deq1G6\"/-I%diffGI*prot
ectedGF)6$-I\"xGF%6#I\"tGF%F.,&-I\"yGF%F-\"\"(F+!\"(" }{TEXT 204 0 "" 
}}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 29 "deq2  := diff(y(t),t)
=25*x(t)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n       -y(t)-x(t)
*z(t);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I%deq
2G6\"/-I%diffGI*protectedGF)6$-I\"yGF%6#I\"tGF%F.,(-I\"xGF%F-\"#DF+!\"
\"*&F0\"\"\"-I\"zGF%F-F5F3" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0
 "" {MPLTEXT 1 202 38 "deq3 := diff(z(t),t)=x(t)*y(t)-3*z(t);" }
{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I%deq3G6\"/-I%
diffGI*protectedGF)6$-I\"zGF%6#I\"tGF%F.,&*&-I\"xGF%F-\"\"\"-I\"yGF%F-
F3F3F+!\"$" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 
202 36 "ic1   := x(0) = 1, y(0)=20, z(0)=19;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 9 "\n        " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 60 
"\ndSol := dsolve(\{deq1,deq2,deq3,ic1\}, numeric, range=0..80);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 1 "\n" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#>I$ic1G6\"6%/-I\"xGF%6#\"\"!\"\"\"/-I\"yGF%F*\"#?/-I\"z
GF%F*\"#>" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I%dSolG
6\"f*6#I(x_rkf45GF%6)I$resGF%I%dataGF%I%varsGF%I)solnprocGF%I)outpoint
GF%I&ndsolGF%I\"iGF%6#IinCopyright~(c)~2000~by~Waterloo~Maple~Inc.~All
~rights~reserved.GF%F%C*>I8_EnvDSNumericSaveDigitsGF%I'DigitsGF%>F6\"#
9@%/I-_EnvInFsolveGF%I%trueGI*protectedGF=>8(-&I&evalfGF=6#F56#9$>F?-F
BFD>8%`6$I$GetGF%I$SetGF%b6#I+thismoduleGF%6#I%DataGF%F%FKF%F%F%F%I+_m
19531200GF%FQ>8&-_FIFL6#Q(sysvarsF%>8'-FW6#Q/soln_procedureF%@$4-I%typ
eGF=6$F?.I(numericGF=C$@,-I'memberGF=6$FE7+Q&startF%.I&startGF%Q'metho
dF%.I'methodGF%Q%leftF%Q&rightF%Q)leftdataF%Q*rightdataF%Q+enginedataF
%C$>8$-Fen6#-I(convertGF=6$FE.I'stringGF=@&-F\\o6$Fcp.I&arrayGF=O-I%ev
alGF=6$Fcp\"\"\"0FcpQ)procnameF%OFcp-Fco6$FE7&Q%lastF%.I%lastGF%Q(init
ialF%.I(initialGF%C$Fbp@$-F\\o6$Fcp.I%listGF=O7#-I$seqGF=6$/&FU6#,&8*F
dqFdqFdq&FcpF^s/F`s;\"\"!\"\"$3-F\\o6$F?I\"=GF=-Fco6$-I$lhsGF=6#F?7$F^
rF_rC$@%-F\\o6$-I$rhsGF=F^tFer>Fcp-Fen6#/F^r7$Fds-I#opGF=6#FdtYQKiniti
al~values~must~be~specified~in~a~listF%Fbr/F?Q.solnprocedureF%O-Fbq6#F
en/F?FYOFU@%09!I(unknownGF%O-.FiuFDC$>8)-I(pointtoGF=6#&-FW6#Q0soln_pr
oceduresF%6#FdsO-.F`vFDZ%C$>Fcp-FenF^tFhrF%YF%F%F%F%" }{TEXT 204 0 "" 
}}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 
"> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 
1 202 12 "with(plots);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#7fnI(animateG6\"I*animate3dGF%I-animatecurveGF%I&arrowG
F%I-changecoordsGI(_syslibGF%I,complexplotGF%I.complexplot3dGF%I*confo
rmalGF%I,conformal3dGF%I,contourplotGF%I.contourplot3dGF%I*coordplotGF
%I,coordplot3dGF%I-cylinderplotGF%I,densityplotGF%I(displayGF%I*displa
y3dGF%I*fieldplotGF%I,fieldplot3dGF%I)gradplotGF%I+gradplot3dGF%I,grap
hplot3dGF%I-implicitplotGF%I/implicitplot3dGF%I(inequalGF%I,interactiv
eGF%I2interactiveparamsGF%I-listcontplotGF%I/listcontplot3dGF%I0listde
nsityplotGF%I)listplotGF%I+listplot3dGF%I+loglogplotGF%I(logplotGF%I+m
atrixplotGF%I)multipleGF%I(odeplotGF%I'paretoGF%I,plotcompareGF%I*poin
tplotGF%I,pointplot3dGF%I*polarplotGF%I,polygonplotGF%I.polygonplot3dG
F%I4polyhedra_supportedGF%I.polyhedraplotGF%I'replotGF%I*rootlocusGF%I
,semilogplotGF%I+setoptionsGF%I-setoptions3dGF%I+spacecurveGF%I1sparse
matrixplotGF%I+sphereplotGF%I)surfdataGF%I)textplotGF%I+textplot3dGF%I
)tubeplotGF%" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 
1 202 46 "odeplot(dSol,[x(t),y(t),z(t)],0..80,refine=1);" }{MPLTEXT 1 
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