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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 15 "Logistic Models" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "The cell \+
below defines a procedure  -- " }{TEXT 256 6 "cobweb" }{TEXT -1 89 "  \+
-- that can be used to draw cobweb diagrams.\nThis procedure requires \+
three arguments.\n\n" }{TEXT 257 4 "fcn " }{TEXT -1 100 " -- the funct
ion that describes how each term of the sequence is computed from the \+
preceding term.\n\n" }{TEXT 258 5 "first" }{TEXT -1 50 " -- the value \+
of the first term of the sequence.\n\n" }{TEXT 259 1 "n" }{TEXT -1 76 
" -- the number of terms of the sequence to be shown in the cobweb dia
gram \n\n" }{TEXT 260 27 "Evaluate the cell below now" }{TEXT -1 4 ". \+
 \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1488 "with(plots):\nwith
(plottools):\n\nPopModel :=\n     proc(fcn, first, n) \n        if n <
= 1 then first else fcn(PopModel(fcn, first, n-1)) fi:\n     end:\n\nc
obweb := \n     proc(fcn, first, n, top)\n     local blk, rd, blu, frm
, cobweblist, j;\n\n     cobweblist := \{line([first, 0], [first, fcn(
first)])\}:\n\n     for j from 3 to n do\n        cobweblist := cobweb
list union\n            \{line([PopModel(fcn, first, j-2), PopModel(fc
n, first, j-1)],\n                  [PopModel(fcn, first, j-1), PopMod
el(fcn, first, j-1)]), \n             line([PopModel(fcn, first, j-1),
 PopModel(fcn, first, j-1)],\n                  [PopModel(fcn, first, \+
j-1), PopModel(fcn, first, j)])\}\n     od:\n\n     frm := display(\{l
ine([0, 0], [0, top]),\n                     line([0, top], [top, top]
),\n                     line([top, top], [top, 0]),\n                \+
     line([top, 0], [0, 0])\},\n                     color = BLACK,\n \+
                    axes = NONE,\n                     scaling = CONST
RAINED):\n\n     blk := plot(f(p),\n                    p = 0..top,\n \+
                   y = 0..top,\n                    color = BLACK,\n  \+
                  scaling = CONSTRAINED):\n\n     rd  := display(cobwe
blist,\n                    color = RED,\n                    axes = N
ONE,\n                    scaling = CONSTRAINED):\n\n     blu := displ
ay(\{line([0, 0], [top, top])\},\n                    color = BLUE,\n \+
                   axes = NONE,\n                    scaling = CONSTRA
INED):\n\n     display([blk, rd, blu, frm]);   \n  end:" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 133 "The foll
owing cell illustrates how this new procedure can used along with othe
r Maple procedures to investigate long term behavior.  " }{TEXT 261 
16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 359 " f := p -> a * (1 - p / c) * p:\n\n a :=
 3.0:\n c := 1000.0:\n\n  cobweb(f, 50, 30, 1000);\n\n  pop := proc(n)
 option remember;\n         if n = 1 then 50 else f(pop(n-1)) fi\n    \+
     end:\n\n  for k from 1 to 30 \n      do printf(`%4d %10.4f`, k, p
op(k));\n      print();\n      od;\n\n  plot([seq([n, pop(n)], n = 1 .
. 30)], \n        year = 1 .. 30, title = `Population`);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 2 2" 87 }{VIEWOPTS 1 
1 0 1 1 1803 }