{VERSION 2 3 "APPLE_68K_MAC" "2.3" }
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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 40 "Predators and Prey -- Sp
rings and Masses" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 140 "The cell below illustrates how Maple can be used to inve
stigate models like the Predator - Prey and Spring-and-Mass models in \+
this module.  " }{TEXT 256 69 "Evaluate it now and then use it as the \+
basis for further exploration." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 646 "\nwith('plots'):\ninitialp \+
:= 300:\ninitialq := 300:\n\nh     := 0.1:\nsteps := 120:\n\nf := (p, \+
q) -> (0.005 * q - 1) * p:\ng := (p, q) -> (1 - 0.005 * p) * q:\n\np :
= proc(n) option remember;\n     if (n = 1) then\n        initialp\n  \+
   else\n        p(n - 1) + h * f(p(n - 1), q(n - 1))\n     fi:\n     \+
end:\n\nq := proc(n) option remember;\n     if (n = 1) then\n        i
nitialq\n     else\n        q(n - 1) + h * g(p(n - 1), q(n - 1))\n    \+
 fi:\n     end:\n\nrd := plot([seq([n, p(n)], n = 1 .. steps)], 1 .. s
teps, color = red):\nblu := plot([seq([n, q(n)], n = 1 .. steps)], 1 .
. steps, color = blue):\ndisplay([rd, blu]);\n\nplot([seq([p(n), q(n)]
, n = 1 .. steps)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}}{MARK "0 2 1" 69 }{VIEWOPTS 1 1 0 1 1 1803 }