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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 16 "Rossler Analysis" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Restart M
aple and load the linear algebra package." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{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 the r.h.s. of the \+
system." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "f:=-y-z:g:=x+a*y:h:=b-c*z+x*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 19 "_EnvExplicit:=true;" }}}{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 12 "ep2:=eps[2]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 28 "Carry out the linearisation." }}
{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:=jac
obian(u,[x,y,z]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J1:=su
bs(ep1,evalm(J));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J2:=su
bs(ep2,evalm(J));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 72 "Determine the characteristic polynomial for the fi
rst equilibrium point." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "cp1:=collect(charpoly(J1,lambda),la
mbda);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 25 "Evaluate the determinant." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "det(J1);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "Shows the
 instability of the first equilibrium point." }}}}{MARK "19" 0 }
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