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The aim of this paper is to study the dynamical behavior of positive solutions for a system of rational difference equations of the following form: un+1=αun-1/β+γvn-2p, vn+1=α1vn-1/β1+γ1un-2p, n=0,1,…, where the parameters α,β,γ,α1,β1,γ1,p and the initial values u-i,v-i for i=0,1,2 are positive real numbers. [ABSTRACT FROM AUTHOR]

We deal with the form of the solutions for the following systems of rational difference equations xn+1 = (xn-1yn/(±xn-1 ± yn-2)), yn+1 = (xnyn-1/(±yn-1 ± xn-2))> with nonzero real numbers initial conditions. Also we investigate some properties of the obtained solutions and present some numerical examples. [ABSTRACT FROM AUTHOR]

The behavior of well-defined solutions of the difference equation xn = anxn-k/(bn + cnxn-1 · · · xn-k), n ∊ N0, where k ∊ N is fixed, the sequences an, bn and cn are real, (bn, cn) ≠(0, 0), n ∊ N0, and the initial values x-k, . . ., x-1 are real numbers, is described. [ABSTRACT FROM AUTHOR]

The following difference equation Xn = Xn-1Xn-k-1, n ∈ ℕ0, where k, l ∈ ℕ, k < l, gcd(k, l) = 1, and the initial values x-1,…, x-2, x-1 are real numbers, has been investigated so far only for some particular values of k and l. To get any general result on the equation is turned out as a not so easy problem. In this paper, we give the first result on the behaviour of solutions of the difference equation of general character, by describing the long-term behavior of the solutions of the equation for all values of parameters k and l, where the initial values satisfy the following condition min {x-1,…, x-2, x-1}. [ABSTRACT FROM AUTHOR]