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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 22 "Lorenz System Analysis
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Resta
rt Maple and load the linear algebra package." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "Define th
e r.h.s. of the system." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f:=sigma*(y-x):g:=r*x-y-x*z:h:=x*y-
b*z:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 28 "Find the equilibrium points." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "eps:=solve(\{f,g,h\},\{x,y
,z\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ep1:=eps[1];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eps2:=allvalues(eps[2]);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ep2:=eps2[1];" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ep3:=eps2[2];" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "Find the Jacobian \+
matrix at each equilibrium point." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "u:=[f,g,h]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J:=jacobian(u,[x,y,z]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J0:=subs(ep1,evalm(J));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "cp0:=collect(charpoly(J0,lambda),la
mbda);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evs:=eigenvals(J0
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ev1:=evs[1];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ev2:=evs[2];" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ev3:=evs[3];" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "J1:=subs(ep2,evalm(J));" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "Find the characteris
tic polynomial." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 41 "cp2:=collect(charpoly(J1,lambda),lambda);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J2:=subs(ep3,evalm(J));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "Sa
me characteristic polynomial as previous equilibrium point." }}{PARA 
0 "" 0 "" {TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "
cp3:=collect(charpoly(J2,lambda),lambda);" }}}{EXCHG {PARA 0 "" 0 "" 
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