WebConcerning the spectral conditions, we remark that it is well-known that imbedded eigenvalues and resonances are unstable under perturbations. See the recent work by Cuccagna, Pel

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WebOrbital stability If, however, you are thinking in terms of orbital stability, then a simple example would be the dynamical system on R given by x ˙ = x 3 We have that x ( t) = 0 is a fixed point. Its linearised dynamics is x ˙ = 0, hence is trivially orbitally stable. http://scholarpedia.org/article/Stability canine polyarthritis

Orbital Stability - Wikipedia

WebJun 25, 2024 · Using the integrability of the defocusing cmKdV equation, we prove the spectral stability of the elliptic solutions. We show that one special linear combination of the first five conserved quantities produces a Lyapunov functional, which implies that the elliptic solutions are orbitally stable with respect to the subharmonic perturbations. WebJan 2, 2013 · For such a model we prove the existence of standing waves of the form u(t) = e iωt Φ ω, which are orbitally stable in the range σ ∈ (0, 1), and orbitally unstable when σ ⩾ 1. Moreover, we show that for σ ∈ ( 0 , 1 2 ) every standing wave is asymptotically stable in the following sense. WebAug 20, 2024 · For the stability in full space, if they are close to the north or south pole, then all such relative equilibria are spectrally unstable; if they are close to the equator, they are orbitally stable if the number of masses is odd, and they are spectrally unstable if the number of masses is even. five blows