= Overstability
<Overstability> is oscillatory instability: a perturbation grows while continuing to change sign or direction periodically. A real perturbation can contain $e^{\sigma t}(a\cos\omega t+b\sin\omega t)$ with $\sigma>0$ and $\omega\ne0$, corresponding to a complex-conjugate pair of linear growth rates with positive <real part>.
The oscillation period is approximately $2\pi/|\omega|$, while $1/\sigma$ sets the envelope-growth <time>. Successive peak heights can therefore reveal growth even when a short segment of the trace resembles an ordinary oscillation. This differs from a stationary instability with a purely real positive growth rate and from a damped oscillation with a negative envelope growth rate. The distinction is useful when classifying how an equilibrium first becomes unstable as a control parameter changes, including an oscillatory onset associated with a <Hopf bifurcation>.
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