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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 256 21 "Predator Prey System\n
" }{TEXT -1 39 "Example 1, page 545: Rabbits and Wolves" }{MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart; with(DEto
ols):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "SYS:= [ D(R)(t) =  0.08*R(
t) - 0.001*R(t)*W(t),\n        D(W)(t) = -0.02*W(t) + 0.00002*R(t)*W(t
)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "dfieldplot(SYS,[R(t)
,W(t)],t=0..1,R=0..2000,W=0..150);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "ODE := D(W)(R) = (-0.02*W(R) + 0.00002*R*W(R))/(0.08*
R - 0.001*R*W(R));   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "si
mplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(ODE,W(
R));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "dsolve(\{ODE,W(500)
=25\}); WW := rhs(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "pl
ot(WW,R=0..5000,view=[0..5000,0..200]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 156 "phaseportrait(SYS,[R(t),W(t)],t=0..250,[[W(0)=25,R(0
)=500],\n[W(0)=100,R(0) = 1200]],linecolor=[blue,black],thickness=2,st
epsize=0.1,\nview=[0..5000,0..200]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 137 "SYS1:= [ D(R)(t) =  0.08*R(t) - 0.001*R(t)*W(t),\n  \+
      D(W)(t) = -0.02*W(t) + 0.00002*R(t)*W(t),\n         R(0)=500, W(
0) = 25        ];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "sln := dsolve(
SYS1,[R(t),W(t)],type=numeric);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "with(plots):\nodeplot(sln,[[t,R(t)/1000],[t,W(t)/80]]
,0..400);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "12
" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }