Many thanks now I solved Lorentz equations and I plot in 2D. But when I try to plot in 3D phase space I get result different about the true "spirals "
This is what I did
from sage.calculus.desolvers import desolve_system_rk4
x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t')
sigma=10
b=8/3
r=10
P=desolve_system_rk4([sigma*(y-x),r*x-y-x*z,x*y-b*z],[x,y,z],ics=[0,0,1,0]
,ivar=t,end_points=20)
py=list_plot3d([[x,y,z] for t,x,y,z in P],plotjoined=True,axes_label=True)
show(py)
Please find the attached file to see the plot
Thanks
Doaa
On 11 October 2012 12:55, David Joyner <[email protected]> wrote:
> On Thu, Oct 11, 2012 at 7:28 AM, Doaa El-Sakout <[email protected]> wrote:
> > Dear David,
> > I would like to plot x(t) against t similar for y and z
> > and after that plot [x,y,z] in phase space
> > So I want know the solution first for the system
> > before plot the result.
> > Thanks
> > Doaa
>
>
> Your system is similar to one used to model a Zombie attack (which is
> in turn borrowed from an infection model). The sage code is here:
> http://wdjoyner.org/zombies/love-war-zombies.sage
> The commands I think you want are towards the bottom.
> Slides going into more detail is here:
> http://wdjoyner.org/zombies/love-war-zombies_slides.pdf
> There is even a video:-)
>
> http://www.mosaic-web.org/go/MCAST/videos/MCAST-2011-04-22/lib/playback.html
>
>
> >
> >
> > On 11 October 2012 10:55, David Joyner <[email protected]> wrote:
> >>
> >> On Thu, Oct 11, 2012 at 3:20 AM, Doaa El-Sakout <[email protected]>
> wrote:
> >> > Hi everyone,
> >> > I try to solve a system of ODE by sage as follows
> >> >
> >> > x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t')
> >> > sigma=10
> >> > b=8/3
> >> > r=10
> >> > x= function('x',t)
> >> > y= function('y',t)
> >> > z= function('z',t)
> >> > d1=(diff(x,t)-sigma*(y-x)==0)
> >> > d2=(diff(y,t)-r*x+y+x*z==0)
> >> > d3=(diff(z,t)-x*y+b*z==0)
> >>
> >> This makes it non-linear. Did you intend to type that?
> >>
> >> > sol=desolve_system([d1,d2,d3],[x,y,z],ics=[0,1,0],ivar=t);show(sol)
> >> >
> >> > But I got the following error
> >> >
> >> > TypeError: unable to make sense of Maxima expression
> >> >
> >> >
> 'x(t)=ilt((?g3817-10*laplace(x(t)*z(t),t,?g3817)+1)/(?g3817^2+11*?g3817-90),?g3817,t)'
> >> > in Sage
> >> >
> >> >
> >> >
> >> > Any suggestion
> >> > Doaa
> >> >
> >> > --
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<<attachment: phase_space .jpeg>>
