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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 22 "Modelling Competition." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "Build a Maple model of \+
Lotka-Volterra Competition" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 38 "dN1/dt = (r1N1/K1)*(K1 - N1 -alpha*N2)" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "dN2/dt = (r2N2/
K2)*(K2 -N2 -beta*N1)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 117 "Look at the conditions for stability by adjusting K1,
K2,alpha and beta in the parms statement and rerun the model..  " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 104 "Test the
 invasibility criterion for coexistence by using the appropriate initi
al condition for invasion." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 118 "Does stability as viewed in the direction field \+
in the phase portrait match what you see in your invasion experiments?
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with (DEtools):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eq1:=diff(N1(t),t) =   ;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eq2:= diff(N2(t),t) =  ;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "parms:=r1=0.1,r2=0.2,K1=100
0,K2=800, alpha=0.5,beta=0.9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 50 "rate_equations:=[subs(parms,eq1),subs(parms,eq2)];" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "vars:= [N1(t),N2(t)];" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "init:=[0,10,10];" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "domain:=0..80;" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "DEpl
ot(rate_equations,vars,t=domain,\{init\},scene=[t,N1]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "DEplot(rate_equations,vars,t=domain
,\{init\},scene=[t,N2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 
"DEplot(rate_equations,vars,t=domain,\{init\},scene=[N1,N2],arrows=THI
N);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Build the equivalent model
 for mutualism and look at its stability." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }