I have an equation:
$V_{t+1}=V_t+r(S(V_t))$. r is a constant
when$(r=?)$ is $V$ asymptotically stable and when otherwise?
What I tried is, finding equilibrium points, I got: $S(V_t)=0 $ and $r=0$.
$|f'(Eq.)|$=$ $1+0$ which is not so helpful.
Any comments?