Roots, or eigenvalues, of the characteristic equation for each of the three locusts
| . | Roots of characteristic equation . | . | . | ||
|---|---|---|---|---|---|
| Locust . | λ1,2 . | λ3 . | λ4 . | ||
| `R' | −4.9±62i | 5.0 | −2.5 | ||
| `G' | −7.1±100i | 5.7 | −3.5 | ||
| `B' | −5.3±55i | 6.0 | −3.9 | ||
| . | Roots of characteristic equation . | . | . | ||
|---|---|---|---|---|---|
| Locust . | λ1,2 . | λ3 . | λ4 . | ||
| `R' | −4.9±62i | 5.0 | −2.5 | ||
| `G' | −7.1±100i | 5.7 | −3.5 | ||
| `B' | −5.3±55i | 6.0 | −3.9 | ||
Note that each locust has one pair of complex conjugate roots(λ1,2) with negative real parts (describing a stable oscillatory mode), one positive real root (λ3, describing an unstable divergence mode), and one negative real root (λ4,describing a stable subsidence mode).
The real parts of the roots define the damping of the modes.
Imaginary parts define the angular frequency of an oscillatory mode.