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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 16 "Worked Example 3" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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,b)->(1+b)*x-x^3;" }{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,b),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],b);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "s2:=dg(eps[2],b);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "s3:=dg(eps[3],b);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "solve(abs(s1)<1,b);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "solve(abs(s2)<1,b);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "Obtain the bifurcation diagram.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "p1:=orbit(g,-0.2,-1,2,100,250,400):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 34 "p2:=orbit(g,0.2,-1,2,100,250,400):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(\{p1,p2\});" }}}}
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