= Solution
The constant solutions are <fixed points> of $G(u)=u^2(1+u)/2$. Solving $G(u)=u$ gives $u(u+2)(u-1)=0$, hence $u_*=0,-2,1$. For a <discrete dynamical system>, a small perturbation satisfies $\eta_{n+1}=G'(u_*)\eta_n+O(\eta_n^2)$, where
$$
G'(u)=u+\frac32u^2,\qquad G'(0)=0,\quad G'(-2)=4,\quad G'(1)=\frac52.
$$
A multiplier of magnitude less than one contracts perturbations; a multiplier greater than one expands them. Therefore \b[$u=0$ is asymptotically stable, while $u=-2$ and $u=1$ are unstable]. In particular, if $|u|\leq1/2$, then $|G(u)|\leq(3/4)|u|^2\leq(3/8)|u|$, proving convergence to zero without relying solely on the vanishing linear multiplier.
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