- #1
Oliver321
- 59
- 5
I was dealing with nonlinear systems of differential equations like the Lorenz equations (https://en.wikipedia.org/wiki/Lorenz_system). Now there is a trapping region of this system defined by the ellipsoid ρx^2+σy^2+σ(z-2ρ)^2<R.
I wondered how this region is found and I found out that a Lyapunov function is used.
However, I tried to do it another way. I defined r=√(x^2+y^2+z^2). Now I thought: when d/dt r <0 the radial velocity points inward and so there is a trapping region. I calculated this but the result was completely different.
Why doesn’t it work with my way?
Thanks for every awnser!
I wondered how this region is found and I found out that a Lyapunov function is used.
However, I tried to do it another way. I defined r=√(x^2+y^2+z^2). Now I thought: when d/dt r <0 the radial velocity points inward and so there is a trapping region. I calculated this but the result was completely different.
Why doesn’t it work with my way?
Thanks for every awnser!