 Solution

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

λ_{1}, λ_{2} \in R, λ_{1} < 0, λ_{2} < 0.

Both exponential modes decay as

t \to \infty

, so the equilibrium is asymptotically stable. Generic linear orbits approach tangent to the eigenvector for the less negative eigenvalue; the eigenvector directions themselves are invariant straight lines. There is no rotation because both eigenvalues are real.

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