{VERSION 2 3 "APPLE_68K_MAC" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{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 -1 -1 
-1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 
0 0 1 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 256 "" 0 "" {TEXT -1 43 "Sequences -- Classifying
 Equilibrium Points" }}{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.\n
This procedure requires three arguments.\n\n" }{TEXT 257 4 "fcn " }
{TEXT -1 100 " -- the function that describes how each term of the seq
uence 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 diagram \n\n" }{TEXT 260 27 "Evaluate the ce
ll 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\ncobweb := \n     proc(fcn, first, \+
n, top)\n     local blk, rd, blu, frm, cobweblist, j;\n\n     cobwebli
st := \{line([first, 0], [first, fcn(first)])\}:\n\n     for j from 3 \+
to n do\n        cobweblist := cobweblist union\n            \{line([P
opModel(fcn, first, j-2), PopModel(fcn, first, j-1)],\n               \+
   [PopModel(fcn, first, j-1), PopModel(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(\{line([0, 0], [0, top]),\n         \+
            line([0, top], [top, top]),\n                     line([to
p, top], [top, 0]),\n                     line([top, 0], [0, 0])\},\n \+
                    color = BLACK,\n                     axes = NONE,
\n                     scaling = CONSTRAINED):\n\n     blk := plot(f(p
),\n                    p = 0..top,\n                    y = 0..top,\n
                    color = BLACK,\n                    scaling = CONS
TRAINED):\n\n     rd  := display(cobweblist,\n                    colo
r = RED,\n                    axes = NONE,\n                    scalin
g = CONSTRAINED):\n\n     blu := display(\{line([0, 0], [top, top])\},
\n                    color = BLUE,\n                    axes = NONE,
\n                    scaling = CONSTRAINED):\n\n     display([blk, rd
, blu, frm]);   \n  end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 133 "The following cell illustrates how this \+
new procedure can used along with other Maple procedures to investigat
e long term behavior.  " }{TEXT 261 16 "Evaluate it now." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 337 " f \+
:= p -> 4.0 * (1 - .001 * p) * p:\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 %1
0.4f`, k, pop(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 8" 75 }
{VIEWOPTS 1 1 0 1 1 1803 }