 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2012/7/a/iii/solution

λ_{1}, λ_{2} \in R, λ_{1} λ_{2} < 0.

The negative eigenvalue gives a stable manifold direction and the positive eigenvalue an unstable manifold direction. Perturbations along the latter grow, so the equilibrium is unstable even though there are special trajectories approaching it.

 New to topics? Read the docs here!