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-1 74 "Competing Species:  Solve for the equilibria, then construct a \+
phase plot." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 54 "eqns:=\{2*x*(1-(1/2)*x)-x*y=0,3*y*(1-(1/3)*y)-2*x*
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "de:=[diff(x(t),t)=2*x(t)*(1-(1/2)*x
(t))-x(t)*y(t),diff(y(t),t)=3*y(t)*(1-(1/3)*y(t))-2*x(t)*y(t)];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#deG7$/-%%diffG6$-%\"xG6#%\"tGF-,&*&
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" 0 "" {TEXT -1 293 "Here we see that the origin is a source, (2,0) an
d (3,0) are sinks, and (1,1) is a saddle (Verify this analytically by \+
using the Jacobian).  This analysis tells us that, for almost every in
itial condition, one population will die off and the other population \+
will go to its carrying capacity. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
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