An equilibrium point $x^* ∈X$ for an ODE or a DE is stable (S) if $$∀ε > 0, ∃δ>0$$ s.t. $t_0 ∈ T$, $x_0 ∈ X$, $\|x_0−x^*\|_{I\!R^n} < δ =⇒ \|x(t;t_0,x_0)−x^*\|_{I\!R^n} ≤ ε$ $∀t ∈ T$
If it is not stable it is unstable (U).
If this is the definition, why do we say that B is unstable? In the end we can easily pick $$δ,ε>0 ~~s.t.~~ t_0 ∈ T, x_0 ∈ X, ||x_0−x^*||_{I\!R^n} < δ =⇒ \|x(t;t_0,x_0)−x^*\|_{I\!R^n} ≤ ε~~∀t ∈ T$$
Both from the right where it is also A.S. and from the left. I do not understand why B in the phase diagram below is unstable if the definition of eq point is as I stated above. Can you help me?