Therefore (27) guarantees [lambda][member of] {z[alpha](z) : [absolute value of z] < 1} and consequently, (23) is

asymptotically stable.

[k.sub.a](L,[p.sub.2])) behaves

asymptotically as [p.sub.1] (resp.

Stepanov and Weyl Generalizations of (

Asymptotically) Almost Periodic and Almost Automorphic Functions

This clearly indicates the coexistence of two locally

asymptotically stable equilibria when [R.sup.*.sub.1] < 1, confirming that model (1) undergoes the phenomenon of backward bifurcation with one stable high-criminality equilibrium [P.sup.+.sub.h] (higher, solid curve in Figure 2), one unstable high-criminality equilibrium [P.sup.-.sub.h] (lowest dashed curve in Figure 2), and one low-criminality equilibrium [P.sub.l].

Further, (i) if [R.sub.0] < 1, the disease-free equilibrium [E.sub.02]([K.sub.p], 0, [[bar.S].sub.h], 0, 0) is locally

asymptotically stable and (ii) if [R.sub.0] > 1, the disease-free equilibrium [E.sub.02]([K.sub.p], 0, [[bar.S].sub.h], 0, 0) is unstable and the endemic equilibrium [E.sup.*]([S.sup.*.sub.p], [I.sup.*.sub.p], [S.sup.*.sub.h], [E.sup.*.sub.h], [I.sup.*.sub.h]) exists and is locally

asymptotically stable.

Then, the zero solution is

asymptotically stable whenever [mathematical expression not reproducible], and [mathematical expression not reproducible].

Liu, "

Asymptotically almost periodic solutions of stochastic functional differential equations," Applied Mathematics and Computation, vol.

If [mu]x [less than or equal to] l holds, then the point [E.sup.*] is globally

asymptotically stable.

(i) The infection equilibrium without humoral immunity [E.sub.1] is globally

asymptotically stable if [R.sub.0] > 1, [R.sub.1] [less than or equal to] 1, and

of system (1) is globally

asymptotically stable, if the following matrix

Moreover, similar to the cases in the AdS space and dS space, the specific heat capacity of the black hole in the

asymptotically flat space can be expressed as [c.sub.v] ~ [(T - [T.sub.c]).sup.-2/3] [29], where [T.sub.c] denotes the critical temperature.

For a given [gamma] > 0, the closed-loop system (12) can reach consensus with the desired [H.sub.[infinity]] disturbance attenuation index y, if the following n-1 subsystems are simultaneously

asymptotically stable with [mathematical expression not reproducible] for i = 1, 2, ..., n-1.