Global asymptotic behavior of the difference equation yn+1=α⋅e−(nyn+(n−k)yn−k)β+nyn+(n−k)yn−k

In this work, we study the boundedness and the global asymptotic behavior of the solutions of the difference equation yn+1=α⋅e−(nyn+(n−k)yn−k)β+nyn+(n−k)yn−k,n=0,1,…, where αα and ββ are positive real numbers, k∈{1,2,…}k∈{1,2,…} and the initial conditions y−k,…,y−1,y0y−k,…,y−1,y0 are arbitrary numbers.