In non linear system problem
I got origin is an asymptotically stable equalibrium point using liapunov function whereas when i solved respective linearized system then i got same point is stable but not asymptotically stable equli. point.
Is there any problem like this?
The nonlinear system can be asymptotically stable at 0 even though the linearised system is not, for instance:
x' = -x^3
is asymptotically stable at 0, the Lyapunov function V(x) = x^2 works, but the linearised system x' = 0 is only stable, not asymptotically stable.
Hi,
For the logistic map, we achieved other determinism in the results with scales of physical dimensions. It is in our report from beginning of this year.
Since dynamics, time could be a plausible unit here, if you don't know the underlying equation.
Kind regards
Hi. What do you mean for stable but not asymptotically stable? If the equilibrium point is not hyperbolic, the linearization around it will not "mimic" the local dynamic of the nonlinear system. Pay a look to the hypothesis of Hartman-Grobman theorem. Good luck with your problem.
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