Consider the systems $$ \begin{cases}\dot{x}=-y-2x-4x^3\\\dot{y}=-2y-x\end{cases}\text{ and }\begin{cases}\dot{x}=-x-7y\\\dot{y}=-2y+10x\end{cases}. $$ Decide whether they are topologically equivalent or not.
I am not sure how to decide that.
Both systems have equilibrium $(0,0)$. If I linearize the first system at $(0,0)$ then for the linearized system, the equilibrium $(0,0)$ is a stable one. For the second system, $(0,0)$ is a stable equilibrium, too.
That's all I can say by now. Maybe there is a theorem, corollar, lemma etc. that only need these information to say something about topological equivalence. Or you just have an idea. Thanks!