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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 35 "Phase Portrait for a Li
enard System" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart:\nw
ith(plots):\nwith(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "De
fine the differential equation using parameters:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 83 "LienardDE := [diff(x(t),t) = y(t),\n         \+
  diff(y(t),t) = (1-x(t)^4)*y(t)-x(t)];" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 120 "Plot the phaseportrait using Runge-Kutta method;  the in
itial conditions are given in the first line and can be changed." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "IC:=[[x(0)= 0,y(0)=1.5],[x(0
)= 0,y(0)=2.3]];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "DEplot(Lienard
DE, [x(t),y(t)], t=0..10,  \n  IC,linecolour=BLUE, x=-3..3, y=-3..3, s
tepsize=0.05,\n  arrows=NONE, method=classical[rk4], title=`Lienard Sy
stem`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 80 "You could try changing the parameters in \+
the equation to get different examles. " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Plot x versus
 t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 209 "ICt:=[[x(0)= 0,y(0)=
1.5]];\nDEplot(LienardDE, [x(t),y(t)], t=0..20,  \n  ICt,linecolour=BL
UE, x=-3..3, y=-4..4, stepsize=0.05,\n  arrows=NONE, method=classical[
rk4],scene=[t,y], \n  title=`Lienard System: (t,y)`);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 58 "Plot the vector field for   x' = x(2-x-y)
,  y' = y(3-x-2y)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "fieldp
lot([y,(1-x(t)^4)*y(t)-x(t)],  x = -3..3, y=-3..3);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 9 }{VIEWOPTS 1 1 0 3 
2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }