For homogeneous fields the gradient terms vanish, leaving
$$
\dot n=\gamma-\delta n,
\qquad
\dot c=\alpha n-\beta c.
$$
Thus
$$
\boxed{n_*=\frac\gamma\delta},
\qquad
\boxed{c_*=\frac{\alpha\gamma}{\beta\delta}}.
$$
The homogeneous Jacobian is triangular,
$$
\begin{pmatrix}-\delta&0\\ \alpha&-\beta\end{pmatrix},
$$
with strictly negative eigenvalues $-\delta$ and $-\beta$. The fixed point is therefore linearly stable to homogeneous perturbations.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 355 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-355/2/a/solution