{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "EXAMPLE: Obtain a phase plot for a nonlinear system of differe ntial equations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 32 "We can solve for the equilibria:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eqns:=\{x*(1-x-y)=0,y*(3-x-2*y)=0\};" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqnsG<$/*&%\"xG\"\"\",(F)F)F(!\"\"% \"yGF+F)\"\"!/*&F,F),(\"\"$F)F(F+*&\"\"#F)F,F)F+F)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(eqns,\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&<$/%\"xG\"\"!/%\"yGF&<$F'/F%\"\"\"<$/F(#\"\"$\"\"#F$<$/ F(F0/F%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "de1:=[diff( x(t),t)=x(t)*(1-x(t)-y(t)),diff(y(t),t)=y(t)*(3-x(t)-2*y(t))];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$de1G7$/-%%diffG6$-%\"xG6#%\"tGF-*&F *\"\"\",(F/F/F*!\"\"-%\"yGF,F1F//-F(6$F2F-*&F2F/,(\"\"$F/F*F1*&\"\"#F/ F2F/F1F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 76 "DEplot(de1,[x(t),y(t)],t=-1..2,x=-2..2,y=-1. .3,dirgrid=[20,20],color=black);" }}{PARA 13 "" 1 "" {GLPLOT2D 416 240 240 {PLOTDATA 2 "6%-%'CURVESG6]dl7%7$$!3%3!#<$!3FW_([DPoI *!#=7$$!3;HGW*f=#z?F*$!3evC^uiJp5F*7$$!3Z`)H5(oeF?F*$!3+L91(41\"f5F*7% 7$$!32z\\\\&)p3:a&))eyZu5F*7$$ !3gE!4G`II\"=F*$!3%HDdYnC31\"F*7%7$$!3-P_,')*f.^\"F*$!3$>TE_$\\\\,#*F- 7$$!3Ioo#3vMvk\"F*$!3qetZ10&)z5F*7$$!3[riV;H(yf\"F*$!3O*e@&o5Ui5F*7%7$ $!3a)4?nZ-nI\"F*$!3%eo!GF'*GZ\"*F-7$$!3VfIaG'R,V\"F*$!3UJ>FP5F&3\"F*7$ $!3E1F\">%p4#Q\"F*$!3SIv+Rsxj5F*7%7$$!3F,%eK*4:/6F*$!3U5<5+l!\\4*F-7$$ !3N4eU![Q;@\"F*$!31H)*)*\\$404\"F*7$$!3up$4$>%Rd;\"F*$!3#3:+xe`Z1\"F*7 %7$$!3N[XD+>LE!*F-$!3yPp>Jt:Z!*F-7$$!3S%3)z?l.@**F-$!3A1.)oE%G&4\"F*7$ $!3q9)G5i;\"*[*F-$!3kRuyw(3_1\"F*7%7$$!3(=I)ym%Q$>qF-$!3R8Lskn$p+*F-7$ $!3Vd[ZQO]dUB5\"F*7$$!3/ '[N6::p9&F-$!3m.1_#)G=k5F*7%7$$!3\"HWCvnLW,$F-$!3=h&HWD!>d*)F-7$$!3[p( fhzb8I$F-$!3)Q/dX(4G/6F*7$$!3g)pb))*G`yHF-$!31'3\"\\9Dri5F*7%7$$!3xvsa sC)p+\"F-$!3AUyI6(e$[*)F-7$$!3;juM&o!G)4\"F-$!3y:#p)GT;06F*7$$!3#y`JF? 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