Solution Curves ( DEplot3d )

Replace the question marks ( %? ) in the following input regions to create the direction field for your model.

> DOMAIN := t = 0 .. 30 ; # specify reasonable interval for indep var

> WINDOW := x = -20 .. 20,

> y = -25 .. 25,

> z = 0 .. 50;

>

> IC1 := [ x(0) = 1, y(0) = 0, z(0)=0 ] ;

> IC2 := [ x(0) = 1.001, y(0) = 0, z(0) = 0 ] ;

>

> P1x:= DEplot( MODEL, VAR, DOMAIN, [ IC1 ], stepsize=0.01,

> scene=[ t, x ], arrows=NONE, linecolor=BLUE ):

> P1y:= DEplot( MODEL, VAR, DOMAIN, [ IC1 ], stepsize=0.01,

> scene=[ t, y ], arrows=NONE, linecolor=BLUE ):

> P1z:= DEplot( MODEL, VAR, DOMAIN, [ IC1 ], stepsize=0.01,

> scene=[ t, z ], arrows=NONE, linecolor=BLUE ):

>

> P2x:= DEplot( MODEL, VAR, DOMAIN, [ IC2 ], stepsize=0.01,

> scene=[ t, x ], arrows=NONE, linecolor=RED ):

> P2y:= DEplot( MODEL, VAR, DOMAIN, [ IC2 ], stepsize=0.01,

> scene=[ t, y ], arrows=NONE, linecolor=RED ):

> P2z:= DEplot( MODEL, VAR, DOMAIN, [ IC2 ], stepsize=0.01,

> scene=[ t, z ], arrows=NONE, linecolor=RED ):

> display( [ P1x, P2x ] , title = `x Solution Curves for 2 Lorenz Systems` );

>

> display( [ P1x, P2x ] , title = `y Solution Curves for 2 Lorenz Systems` );

>

> display( [ P1y, P2y ] , title = `z Solution Curves for 2 Lorenz Systems` );

Based on these graphs, it appears that the solutions are very similar until t=25. At this time, the solutions appear to be quite different.

>