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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT -1 17 "Bambi vs the Lawn" }{TEXT 256 20 ":  problem 1.6 (p43)" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "restart;  with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "  \+
" }}{PARA 0 "" 0 "" {TEXT -1 38 "important constants (rates are annual
)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "max_grass_density := \+
3000;\nmax_grass_growth_rate := 0.8;\nmax_deer_eat_grass_rate := 1.2;
\nmax_deer_reproduce_rate := 1.5;\ndeer_death_rate := 1.1;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 67 "30-year
 simulation (timestep = 1 for yearly, 365 for daily updates)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "timestep := 1;\nfor y from 1
 to 31*timestep do\n if (y=1) then\n" }{TEXT -1 19 "initial population
s" }{MPLTEXT 1 0 56 "\n  deer_pop[1] := 100;\n  grass_density[1] := 30
00;\n else" }{TEXT -1 53 "\nnonlinear growth rates (read the problem c
arefully)\n" }{MPLTEXT 1 0 290 "  grass_growth_rate := max_grass_growt
h_rate *       ((max_grass_density-grass_density[y-1])/max_grass_densi
ty);\n\n  grass_eaten_rate := max_deer_eat_grass_rate * (grass_density
[y-1]/max_grass_density);\n\n  deer_growth_rate := max_deer_reproduce_
rate * (grass_density[y-1]/max_grass_density);" }{TEXT -1 30 "\npopula
tion update:  grass\n   " }{MPLTEXT 1 0 125 " grass_density[y] := gras
s_density[y-1] + \n(grass_growth_rate*grass_density[y-1] - grass_eaten
_rate*deer_pop[y-1])/timestep;\n" }{TEXT -1 24 "population update:  de
er" }{MPLTEXT 1 0 125 "\n  deer_pop[y] := deer_pop[y-1] + (deer_growth
_rate*deer_pop[y-1] -deer_death_rate*deer_pop[y-1])/timestep;\n\n end \+
if;\nend do:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 10 "make plots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
125 "plot1 := [[(n-1)*timestep, deer_pop[n*timestep]] $n=1..31]:\nplot
2 := [[(n-1)*timestep, grass_density[n*timestep]] $n=1..31]:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "plot([plot1,plot2],title=\"
deer & grass\",style=point,symbol=[circle,cross],legend=[\"deer\", \"g
rass\"]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 \+
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