in this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.

the main objective of this paper is to study the boundedness character, the periodicity character, the convergenceand the global stability of the positive solutions of the nonlinear rational difference equation/ , n 0,1,2,....0 01      kii n ikin i n i x  x b  xwhere the coefficients i i b , ,  together with the initial conditions ,.... , , 1 0 x x x k  are arbitrary...

Recently there has been a great deal of interest in studying the behaviour of rational difference equations. One of the properties which has attracted considerable attention from the experts in the research field is the boundedness character (see, e.g. [1–32] and the related references therein). This paper studies the boundedness character of positive solutions of the recursive equation yn = A+...

The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation xn+1 = α0xn + α1xn−l + α2xn−m + α3xn−k β0xn + β1xn−l + β2xn−m + β3xn−k , n = 0, 1, 2, · · · where the coefficients αi, βi ∈ (0,∞) for i = 0, 1, 2, 3, and l,m, k are positive integers. The initial conditions x...

The boundedness character of positive solutions of two nonlinear fourth-order difference equations, which are particular cases of two large classes of difference equations by Stević, are studied in this paper.

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

This paper studies the boundedness character of the positive solutions of the difference equation x(n+1) = A + x(n)^p/(x(n-1)^q*x(n-2)^r), no, where the parameters A, p, q and r are positive numbers.

The present document is devoted to structural properties of neural population dynamics and especially their differential flatness. Several applications of differential flatness in the present context can be envisioned, among which: trajectory tracking, feedforward to feedback switching, cyclic character, positivity and boundedness.