Normal forms for nonautonomous difference equations

Nonautonomous difference equations: Open problems and conjectures

Periodicity Detection in Nonautonomous Difference Equations

System identification for nonlinear differential and difference equations has lagged far behind the linear case, due to the greater complexity of the task. Takens’ Theorem [1,10] of 25 years ago opened a new avenue of investigation, introducing geometric methods that were essential for nonlinear problems. The ramifications of this result have unfolded in an area that has become known as attract...

On Global Attractivity of a Class of Nonautonomous Difference Equations

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn p ryn−s / q φn yn−1, yn−2, . . . , yn−m yn−s , n ∈ N0, with p ≥ 0, r, q > 0, s,m ∈ N and positive initial values, and present some sufficient conditions for the parameters andmaps φn : R m → R , n ∈ N0, under which every positive solution to the equation converges to zero or a u...

Strictly Increasing Solutions of Nonautonomous Difference Equations Arising in Hydrodynamics

The paper provides conditions sufficient for the existence of strictly increasing solutions of the second-order nonautonomous difference equation x n 1 x n n/ n 1 2 x n − x n − 1 h2f x n , n ∈ N, where h > 0 is a parameter and f is Lipschitz continuous and has three real zeros L0 < 0 < L. In particular we prove that for each sufficiently small h > 0 there exists a solution {x n }n 0 such that {...

On a Class of Nonautonomous Max-Type Difference Equations

and Applied Analysis 3 This paper is devoted to the study of the following nonautonomous max-type difference equation with two delays: xn max { fn x n−k , B x β n−m } , n ∈ N0, 1.7 where k,m ∈ N, α, β ∈ R are fixed and fn n∈N0 is a positive sequence with a finite limit. Inspired by the methods and proofs of the above-mentioned papers, here we try to find some sufficient conditions such that eve...