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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "To draw a phase plane diag
ram  for the system" }}{PARA 0 "" 0 "" {TEXT -1 4 "    " }{OLE 1 4612 
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "First you need to load the package
s linalg and DEtools" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "wit
h(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools)
:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Enter the equations as follo
ws" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "A:=diff(x(t),t)=.2*x-
.004*x^2-.003*x*y; " }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 39 "B:=diff(y(t),t)=.1*y-.001*y^2-.003*x*y;" 
}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
41 "Plot the phase plane graph as shown below" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 63 "DEplot(\{A,B\},\{x(t),y(t)\},0..100,x=0..50,y=0.
.100,stepsize=.1); " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 104 "Look at the phase plane graph and choose some \+
initial points for the curves. In this example I have used" }}{PARA 0 
"" 0 "" {TEXT -1 54 "(50,60),(10,15),(5,10),(50,75),(0,100),(50,0),(20
,40)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 189 "DEplot(\{A,B\},\{x(t),y(t)\},0..100,[[x(0)=50,y(0)=6
0],[x(0)=10,y(0)=15],[x(0)=5,y(0)=10],[x(0)=50,y(0)=75],[x(0)=0,y(0)=1
00],[x(0)=50,y(0)=0],[x(0)=20,y(0)=40]],x=0..50,y=0..100,stepsize=.1);
 " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 138 "To plot the solution curves of x and y against t use the \"sce
ne\" command. The following example shows the solution curves of x aga
inst t. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "DEplot(\{A,B\}
,\{x(t),y(t)\},0..100,[[x(0)=50,y(0)=60],[x(0)=10,y(0)=15],[x(0)=5,y(0
)=10],[x(0)=50,y(0)=75],[x(0)=50,y(0)=0],[x(0)=20,y(0)=40]],x=0..50,y=
0..100,scene=[t,x(t)],stepsize=.1); " }}{PARA 13 "" 1 "" {TEXT -1 0 "
" }}}}{MARK "13" 0 }{VIEWOPTS 1 1 0 1 1 1803 }