# stable equilibrium

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## sta·ble e·qui·lib·ri·um

equilibrium in which, after every small perturbation, the original state will tend to be restored.
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In two and three dimensions, there are only two possible dynamics near a stable equilibrium. Either the flow is directly downhill, or it spirals down like water near a sink drain--or air and debris near a tornado.
where [[xi].sub.1], [[xi].sub.2] [member of] R, [N.sub.0], [B.sub.0] are parameters of manipulator system, and the system has a globally asymptotically stable equilibrium at [[xi].sub.*] and [x.sub.*] = [pi]([[xi].sub.*]).
As a closed set, the set Im(EC) has the boundary given by images of some stable equilibrium points of the system through the energy-Casimir mapping.
The solid curve stands for the stable equilibrium and the dashed curve stands for the unstable equilibrium.
(1) If 0 < y < ([c.sub.1] + [f.sub.1])/(a[DELTA][pi] + [f.sub.1] - [E.sub.1]), then there is a stable equilibrium solution for RDE named x = 0 after taking x = 0 and x = 1 into formula (9) and concluding [a.sub.11] < 0 and [a.sub.11] > 0 respectively.
Caption: Figure 2: An asymptotically stable equilibrium for [tau] = [[tau].sub.1] = [[tau].sub.2] = [[tau].sub.3] = 0.
As the time delay increases to the critical value, it can cause a stable equilibrium to become unstable and Hope bifurcation can occur.
Coexistence between Stable Equilibrium Point and Limit Cycle.
Caption: FIGURE 1: (a) Stable equilibrium [E.sub.l].
Also, as the value of recovery rate increases the infected cells revert to the healthy cells more rapidly and converge to stable equilibrium. We can see that the infection would always keep stability when the cure rate [gamma] is larger.
Bourguignon (1981) shows that, for a given proportion of rich a.sub.2 satisfying 0<[a.sub.2]<[bar.A], the possible equilibria are pairs ([k.sub.1],[k.sub.2]) each consisting of an unstable equilibrium [k.sub.1] and a stable equilibrium [k.sub.2] with [k.sub.2] > [k.sub.1].

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