Similar to the discussion of Theorems 16 and 17, we can prove that the system (2) has an order one periodic solution which passes through a point M [member of] [bar.BD] and is

orbitally asymptotically stable.

Because [[GAMMA].sub.**] is unique and

orbitally attractive, there exists a [T.sub.0] such that [rho]([pi](t, [p.sub.0]), [[GAMMA].sub.**]) < [[epsilon].sub.0] for [for all][[epsilon].sub.0] > 0 and [p.sub.0] [member of] M([p.sub.0] > [y.sub.H]), set [p.sub.**] = [[GAMMA].sub.**] [intersection] M.

If 1 - [h.sub.1] - ([[eta].sub.0]/([h.sub.1] + a)) > 0 and [beta] [greater than or equal to] 1, then the periodic solution with initial point [C.sub.0]([h.sub.1], [[eta].sub.0]) (where [[eta].sub.0] > [??]) is

orbitally asymptotically stable.

In Theorem 7, the semitrivial periodic solution (0, [eta](t)) of system (6) is

orbitally asymptotically stable if 1 - [[PHI].sup.-1] < [E.sub.1] (see Figure 4) and the parameters are given A = 5,q = 0.3, B = 3.5, H = 0.4, [E.sub.1] = 0.3, [E.sub.2] = 0.6.

Therefore, the OOPS is

orbitally asymptotically stable.

By Theorem 7, we know that the Hopf bifurcation is supercritical: the bifurcating periodic solutions exist for [tau] < [[tau].sup.*] and they are

orbitally asymptotically stable.

In [12], the authors calculated the masses of baryons with the quadratic mass relations for ground and

orbitally excited states.

The cradle has a low voltage DC motor which rocks it

orbitally.

Materials that can be

orbitally formed include plastics, laminates, composites and other non-metallics, as well as metals.

Automatic flying cut-off saw mounted below table is

orbitally operated and has a manually adjustable envelope.

Climate experts think these

orbitally induced insolation changes are the pacemaker for the glacial cycle, setting the Earth's climate swinging between warm and cold periods.

Llorens-Fuster, "

Orbitally nonexpansive mappings," Bulletin of the Australian Mathematical Society, vol.