AbstractIn this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of the positive solutions of the second-order difference system $$\begin{aligned} x_{n+1}&= \alpha _1 + a e ^{-x_{n-1}} + b y_{n} e ^{-y_{n-1}},\\ y_{n+1}&= \alpha _2 +c e ^{-y_{n-1}}+ d x_{n} e ^{-x_{n-1}} \quad n=0,1,2,\ldots \end{aligned}$$
x
n
+
1
=
α
1
+
a
e
-
x
n
-
1
+
b
y
n
e
-
y
n
-
1
,
y
n
+
1
=
α
2
+
c
e
-
y
n
-
1
+
d
x
n
e
-
x
n
-
1
n
=
0
,
1
,
2
,
…
where $$\alpha _1, \alpha _2, a, b , c,d$$
α
1
,
α
2
,
a
,
b
,
c
,
d
are positive real numbers and the initial conditions $$x_{-1},x_0, y_{-1}, y_0$$
x
-
1
,
x
0
,
y
-
1
,
y
0
are arbitrary nonnegative numbers.
Ulam-Hyers stability results for a novel nonlinear Nabla Caputo fractional variable-order difference system
