In this work, we investigate the global asymptotic stability of the following nonlinear recursive sequence: x n+1 = x n x b n−2 + x b n−3 + x b n−1 + a x n x b n−3 + x b n−2 + x b n−1 + a (1) where a, b ∈ [0, ∞) and the initial values x −3 , x −2 , x −1 , x 0 are arbitrary positive real numbers.

In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation ∆(xn − pnxτ(n)) + f(n, xσ(n)) = qn are obtained. Examples are included to illustrate the results.

General semifinite factor representations of the diffeomorphism group of euclidean space are constructed by means of a canonical correspondence with the finite factor representations of the inductive limit unitary group. This construction includes the quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a non-linear fo...

We study the long-term behavior of positive solutions of the cyclic system of difference equations x (i) n+1 = max n α, (x (i+1) n ) p (x (i+2) n−1 ) q o , i = 1, . . . , k, n ∈ N0, where k ∈ N, min{α, p, q} > 0 and where we regard that x1 n = x (i2) n when i1 ≡ i2 (mod k). We determine the set of parameters α, p and q in (0,∞)3 for which all such solutions are bounded. In the other cases we sh...

The rule of trajectory structure for fourth-order nonlinear difference equation xn 1 x a n−2 xn−3 / x a n−2xn−3 1 , n 0, 1, 2, . . . , where a ∈ 0, 1 and the initial values x−3, x−2, x−1, x0 ∈ 0,∞ , is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4 , 3−, ...

Most clustering algorithmspartition a &fa set based on a dissimilarity relation expressed in t e m of some distance function. When the nature of this relation is conceptual rather than mehic, distance finctions may fail to adequately model dissimilarity. For this reason, we propose to extract dissimilarify relations directlyfrom the data. We exploit some pairs of paffems with known dissimilarit...

We consider the dynamical properties for a kind of fourth-order rational difference equations. The key is for us to find that the successive lengths of positive and negative semicycles for nontrivial solutions of this equation periodically occur with same prime period 5. Although the period is same, the order for the successive lengths of positive and negative semicycles is completely different...

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuousand discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the...

This paper is concerned with the nonlinear advanced difference equation with constant coefficients