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Equilibria correspond to the roots of the right-hand side function $f(z) = 4z - z^3 + C$. As C increases, the graph of $f(z)$ shifts vertically upward.

Conditions: The differential equation is $dz/dt = 4z - z^3 + C$.; $C = 4$, which is greater than the critical value C* ≈ 3.079.

Equilibria correspond to the roots of the right-hand side function $f(z) = 4z - z^3 + C$. As C increases, the graph of $f(z)$ shifts vertically upward.

Conditions: The differential equation is $dz/dt = 4z - z^3 + C$.; $C = 4$, which is greater than the critical value C* ≈ 3.079.

Stability is determined by the direction of the vector field, which is given by the sign of $dz/dt$. Near $z = -2$ and $z = 2$, the arrows on the phase line point toward these equilibria, meaning nearby trajectories converge to them, making them stable.

Conditions: The system is a one-dimensional autonomous ODE.; Stability is inferred from the sign of $dz/dt$ on intervals adjacent to the equilibria.

Stability is determined by the direction of the vector field, which is given by the sign of $dz/dt$. Near $z = -2$ and $z = 2$, the arrows on the phase line point toward these equilibria, meaning nearby trajectories converge to them, making them stable.

Conditions: The system is a one-dimensional autonomous ODE.; Stability is inferred from the sign of $dz/dt$ on intervals adjacent to the equilibria.