= Solution
{c}
Set $z=y-\beta$. Then the <autonomous planar system> becomes
$$
\dot x=z,\qquad \dot z=x^3-x,
$$
which has no $\beta$ dependence. Therefore
$$
\boxed{\text{changing }\beta\text{ translates the entire phase portrait vertically}.}
$$
More precisely, replacing $\beta$ by $\beta+\delta$ sends every trajectory $(x(t),y(t))$ to $(x(t),y(t)+\delta)$, with the same time parametrization. The <equilibrium points>, <nullclines>, <periodic orbits> and <separatrices> all undergo this same <translation>. Their types and orientations are independent of $\beta$, so varying $\beta$ produces no <bifurcation>.
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