Dynamic behavior for a system of neutral functional differential equations
Consider the system of neutral functional differential equations { ( x 1 ( t ) − x 2 ( t − r ) ) ′ = − F ( x 1 ( t ) ) + G ( x 2 ( t − r ) ) , ( x 2 ( t ) − x 1 ( t − r ) ) ′ = − F ( x 2 ( t ) ) + G ( x 1 ( t − r ) ) , where r > 0 , F , G ∈ C ( R ) . It is shown that if F is nondecreasing on R ,...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2009-11, Vol.58 (10), p.2046-2050 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Consider the system of neutral functional differential equations
{
(
x
1
(
t
)
−
x
2
(
t
−
r
)
)
′
=
−
F
(
x
1
(
t
)
)
+
G
(
x
2
(
t
−
r
)
)
,
(
x
2
(
t
)
−
x
1
(
t
−
r
)
)
′
=
−
F
(
x
2
(
t
)
)
+
G
(
x
1
(
t
−
r
)
)
,
where
r
>
0
,
F
,
G
∈
C
(
R
)
. It is shown that if
F
is nondecreasing on
R
, and some additional assumptions hold, then the
ω
limit set of every bounded solution of such a system with some initial conditions is composed of
2
r
-periodic solutions. Our results are new and complement some corresponding ones already known. |
|---|---|
| ISSN: | 0898-1221 1873-7668 |
| DOI: | 10.1016/j.camwa.2009.07.056 |