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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 16 "Worked Example 2" }}
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0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 27 "Load the required packages." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read `maptools.m`:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "De
fine the map." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 22 "g:=(x,a)->4*a*x-a*x^2;" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Fi
nd the equilibrium points." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eps:=solve(x=g(x,a),x);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "Check the
 stability." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 12 "dg:=D[1](g);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "s1:=dg(eps[1],a);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "s2:=dg(eps[2],a);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "solve(abs(s1)<1,a);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "solve(abs(s2)<1,a);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "Stable cobweb for the first equ
ilibrium point." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 31 "cobweb(g,0.2,10,-0.2,0.2,-0.1);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Stable co
bweb for the second equilibrium point." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "cobweb(g,0.2,10,0,1,0.3
);" }}}}{MARK "19" 0 }{VIEWOPTS 1 1 0 1 1 1803 }