On the recursive sequence xn+1 = xn-7/1+xn-3

On the recursive sequence xn+1=

We give a complete picture regarding the behavior of positive solutions of the following important difference equation: xn = 1+ ∑ k i=1αixn−pi / ∑m j=1βjxn−qj , n∈N0, where αi, i∈ {1, . . . ,k}, and βj , j ∈ {1, . . . ,m}, are positive numbers such that ∑ k i=1αi = ∑m j=1βj = 1, and pi, i ∈ {1, . . . ,k}, and qj , j ∈ {1, . . . ,m}, are natural numbers such that p1 < p2 < ··· < pk and q1 < q2 <...

On the Recursive Sequence xn + 1 = A + xpn / xpn − 1

Recently, there has been great interest in studying nonlinear and rational difference equations (cf. [1–23] and the references therein). One of the reasons for this is a necessity for some techniques which can be used in investigating equations arising in mathematical models describing real-life situations in population biology, economics, probability theory, genetics, psychology, sociology, an...

On the Rational Recursive Sequence xn+1=(α-βxn)/(γ-δxn-xn-k)

We study the global stability, the periodic character, and the boundedness character of the positive solutions of the difference equation xn 1 α − βxn / γ − δxn − xn−k , n 0, 1, 2, . . . , k ∈ {1, 2, . . .}, in the two cases: i δ ≥ 0, α > 0, γ > β > 0; ii δ ≥ 0, α 0, γ, β > 0, where the coefficients α, β, γ, and δ, and the initial conditions x−k, x−k 1, . . . , x−1, x0 are real numbers. We show...

On the Recursive Sequence xn 1 max { xn , A } / x 2 nxn − 1

Max-type difference equations stem from, for example, certain models in automatic control theory see 1, 2 . Althoughmax-type difference equations are relatively simple in form, it is, unfortunately, extremely difficult to understand thoroughly the behavior of their solutions, see, for example, 1–41 and the relevant references cited therein. Furthermore, difference equation appear naturally as a...

On the Recursive Sequence xn 1 A x p n − 1 / x q n