{VERSION 6 0 "IBM INTEL NT" "6.0" }
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "eqn1 := xe=1.26*xe-0
.02*xe^2-0.06*xe*ye;\neqn2 := ye=1.06*ye-0.01*ye^2-0.005*xe*ye;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn1G/%#xeG,(*&$\"$E\"!\"#\"\"\"F&F
,F,*&$\"\"#F+F,)F&F/F,!\"\"*($\"\"'F+F,F&F,%#yeGF,F1" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%%eqn2G/%#yeG,(*&$\"$1\"!\"#\"\"\"F&F,F,*&$F,F+F,)F
&\"\"#F,!\"\"*($\"\"&!\"$F,%#xeGF,F&F,F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "solve(\{eqn1,eqn2\},\{xe,ye\});" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6&<$/%#xeG$\"\"!F'/%#yeGF&<$F$/F)$\"\"'F'<$F(/F%$\"#8F'<$
/F)$\"\"\"F'/F%$\"#5F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "w
ith(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected na
mes norm and trace have been redefined and unprotected\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "F := vector([1.26*x-0.02*x^2-0.06*x
*y,1.06*y-0.01*y^2-0.005*x*y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"FGK%'vectorG6#7$,(*&$\"$E\"!\"#\"\"\"%\"xGF.F.*&$\"\"#F-F.)F/F2F.!\"
\"*($\"\"'F-F.F/F.%\"yGF.F4,(*&$\"$1\"F-F.F8F.F.*&$F.F-F.)F8F2F.F4*($
\"\"&!\"$F.F/F.F8F.F4Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "J := jacobian(F,[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"JGK%'matrixG6#7$7$,($\"$E\"!\"#\"\"\"*&$\"\"%F-F.%\"xGF.!\"
\"*&$\"\"'F-F.%\"yGF.F3,$*&$F6F-F.F2F.F37$,$*&$\"\"&!\"$F.F7F.F3,($\"$
1\"F-F.*&$\"\"#F-F.F7F.F3*&$F?F@F.F2F.F3Q(pprint16\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "x:=0;y:=0;\nA0:=J(x,y);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"xG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"y
G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A0GK%'matrixG6#7$7$$\"$E
\"!\"#$\"\"!F.7$F-$\"$1\"F,Q(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "x:=0;y:=6;\nA1:=J(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"xG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG\"\"'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1GK%'matrixG6#7$7$$\"#!*!\"#$\"\"!
F.7$$!#I!\"$$\"#%*F,Q(pprint36\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "eigenvectors(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
7%$\"#!*!\"#\"\"\"<#K%'vectorG6#7$F'$\"+++++v!#5Q(pprint46\"7%$\"#%*F&
F'<#KF*6#7$\"\"!F'Q(pprint5F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 23 "x:=13:y:=0:\nA2:=J(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A
2GK%'matrixG6#7$7$$\"#u!\"#$!#yF,7$$\"\"!F1$\"$&**!\"$Q(pprint96\"" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eigenvectors(A2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$7%$\"$&**!\"$\"\"\"<#K%'vectorG6#7$$!+HN#)eI
!\"*F'Q(pprint76\"7%$\"#u!\"#F'<#KF*6#7$F'\"\"!Q(pprint8F1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x:=10:y:=1:\nA3:=J(x,y);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#A3GK%'matrixG6#7$7$$\"#!)!\"#$!#gF,7$$!\"
&!\"$$\"$!**F2Q)pprint106\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "eigenvectors(A3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$7%$\"+h&eY+\"
!\"*\"\"\"<#K%'vectorG6#7$$\"+bhA;GF&$!+q)zgg*!#5Q)pprint116\"7%$\"+!R
9M&yF1F'<#KF*6#7$$!+&p#H9(*F&$!+MDHtBF1Q)pprint12F3" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 13 "Predator-Prey" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "eq1
:= He=1.04*He-0.0025*He*Le-0.0003*He^2;\neq2:= Le=0.92*Le+0.0023*He*Le
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/%#HeG,(*&$\"$/\"!\"#\"\"
\"F&F,F,*($\"#D!\"%F,F&F,%#LeGF,!\"\"*&$\"\"$F0F,)F&\"\"#F,F2" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/%#LeG,&*&$\"##*!\"#\"\"\"F&F,F
,*($\"#B!\"%F,%#HeGF,F&F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "solve(\{eq1,eq2\},\{He,Le\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%<
$/%#HeG$\"\"!F'/%#LeGF&<$F(/F%$\"+LLLL8!\"(<$/F)$\"+'p3E=\"!\")/F%$\"+
q3EyMF3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }
}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tr
ace have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 62 "F := vector([1.04*x-0.0025*x*y-0.0003*x^2,0.92*y+0.
0023*x*y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGK%'vectorG6#7$,(*
&$\"$/\"!\"#\"\"\"%\"xGF.F.*($\"#D!\"%F.F/F.%\"yGF.!\"\"*&$\"\"$F3F.)F
/\"\"#F.F5,&*&$\"##*F-F.F4F.F.*($\"#BF3F.F/F.F4F.F.Q(pprint06\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J := jacobian(F,[x,y]);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "x:=0;y:=0;\nA0:=J(x,y);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"JGK%'matrixG6#7$7$,($\"$/\"!\"#\"\"\"*&$
\"#D!\"%F.%\"yGF.!\"\"*&$\"\"'F2F.%\"xGF.F4,$*&$F1F2F.F8F.F47$,$*&$\"#
BF2F.F3F.F.,&$\"##*F-F.*&F?F.F8F.F.Q(pprint16\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"xG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A0GK%'matrixG6#7$7$$\"$/\"!
\"#$\"\"!F.7$F-$\"##*F,Q(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "eigenvectors(A0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
7%$\"$/\"!\"#\"\"\"<#K%'vectorG6#7$F'\"\"!Q(pprint36\"7%$\"##*F&F'<#KF
*6#7$F-F'Q(pprint4F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "x:=
133.33;y:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG$\"&LL\"!\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG\"\"!" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 11 "A1:=J(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
A1GK%'matrixG6#7$7$$\"'-+'*!\"'$!'DLLF,7$$\"\"!F1$\"(fmA\"F,Q(pprint56
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eigenvectors(A1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$7%$\"(fmA\"!\"'\"\"\"<#K%'vectorG6#7$$
!+jS,]7!\"*F'Q(pprint66\"7%$\"'-+'*F&F'<#KF*6#7$F'\"\"!Q(pprint7F1" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "x:=34.783;y:=11.826;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG$\"&$yM!\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"yG$\"&E=\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "A2:=J(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G
K%'matrixG6#7$7$$\"(_c*)*!\"($!'v&p)F,7$$\"')*>FF,$\")4++5F,Q(pprint86
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eigenvectors(A2);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6$7%^$$\"++0$y%**!#5$!+LwGN[!#6\"\"\"<#K
%'vectorG6#7$^$$!+[Bpx<!\"*$\"+78M=>F'^$$\"\"!F9$!\"\"F9Q(pprint96\"7%
^$F%$\"+LwGN[F*F+<#KF.6#7$^$F2$!+78M=>F'^$F8$F+F9Q)pprint10F=" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "abs(.9947830500-.4835287633e
-1*I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+x[df**!#5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "12 0 0" 8 }{VIEWOPTS 1 
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