In considered situations we receive
asymptotically stable system.
To overcome this difficulty, we search for an approximate solution to (3.3) which is
asymptotically accurate.
In Section 2, we present the basic information about Stepanov and Weyl generalizations of
asymptotically almost periodic functions and
asymptotically almost automorphic functions (Proposition 4 is the only new contribution in this section).
Hence, for [R.sup.*.sub.1] < [R.sup.thr.sub.1], system (1) will present only the locally
asymptotically stable low-criminality equilibrium [P.sub.l].
The zero solution of system (22) is said to be
asymptotically stable if [parallel]]]x(t)[parallel]]] [right arrow] 0, as t [right arrow] [infinity].
Zhou, "
Asymptotically almost periodicity for a class of Weyl-Liouville fractional evolution equations," Mediterranean Journal of Mathematics, vol.
We recall that E is locally
asymptotically stable if the all eigenvalues [[xi].sub.i] of (40) satisfy the following condition [53-55]:
and we say that the response system can be globally
asymptotically synchronized with the drive system if the zero solution of error system is globally
asymptotically stable.
The main difference between AdS space-time and
asymptotically flat space-time is the famous Hawking-Page phase transition [1]; that is, the AdS background provides a natural constraint box, which makes it possible to form a thermal equilibrium between large stable black hole and hot gas.