I want to use Lorenz'63 for the purpose of testing some algorithms I'm currently researching.
When I defined a system and solved it in Matlab, plot of x-coordinates for explicit and perturbed initial conditions looked like this:
Obviously, there's a big difference in values. But, when I plotted the two solutions $3D$, I got this plot:
Apparently, both solutions lie on the same curve. How is this possible? I would really appreciate any explanation or, even better, some sources from where I can read more about this and get a better feeling of what I'm dealing with.
I tried to find this information in some papers but I couldn't find the explanation.
Thanks a lot!