Affiliation:
1. Democritus University of Thrace
Abstract
In this paper we investigate the behaviour of the solutions of the following
k
-dimensional cyclic system of difference equations with maximum:
x
i
(
n
+
1
)
=
max
{
A
i
,
x
i
p
(
n
)
x
i
+
1
q
(
n
−
1
)
}
,
i
=
1
,
2
,
…
,
k
−
1
,
x
k
(
n
+
1
)
=
max
{
A
k
,
x
k
p
(
n
)
x
1
q
(
n
−
1
)
}
where
n
=
0
,
1
,
…
,
A
i
>
1
, for
i
=
1
,
2
,
…
,
k
, whereas the exponents
p
,
q
and the initial values
x
i
(
−
1
)
,
x
i
(
0
)
,
i
=
1
,
2
,
…
,
k
are positive real numbers.