Assertion: bifurcation | /r/HasProperty | supercritical
Facets:
value: with the evolution of the dynamics
type: OTHER
Source sentences:
text: The limit cycle is orbitally stable if a specific quantity called the first Lyapunov coefficient is negative, and the bifurcation is supercritical.
text: The limit cycle is orbitally stable if a specific quantity called the first Lyapunov coefficient is negative, and the bifurcation is supercritical.
text: The bifurcation can be supercritical or subcritical, resulting in stable or unstable (within an invariant two-dimensional manifold) limit cycle, respectively.
text: If $O_0(\mu_c)$ is NL stable, the bifurcation is supercritical.
text: If the $+$ sign is chosen, the bifurcation is supercritical with the evolution of the dynamics as the parameter crosses $\mu_c$ from below described in the discussion of equation (4).
text: It remains to compute the criticality type of the bifurcation i.e., whether the bifurcation is supercritical or subcritical; the degenerate case that separates supercriticality from subcriticality will be considered in Sec.
text: If $\mathcal{Q}f_{\mu_c}(x_0)<0$, then $x_0$ is NL stable and the bifurcation is supercritical .
text: Bends forward with a parabolic shape as a heavy line close enough to $(\mu_c, x_0)$ when one removes the degeneracy so that the bifurcation is supercritical;
text: The bifurcation can be supercritical or subcritical, resulting in a stable or unstable (within an invariant two-dimensional manifold) closed invariant curve, respectively.
text: Staying away from the strong resonances and assuming that the bifurcation is supercritical, we get a stable closed invariant curve for parameters \(({\rm
text: The (dis)appearing orbits may be stable or unstable, depending, among other factors, on whether the bifurcations are subcritical or supercritical.