Analysis of Qualitative Behavior of Fifth Order Difference Equations

The main aim of this paper is to investigate the stability, global attractivity and periodic nature of the solutions of the difference equationsThe main aim of this paper is to investigate the stability, global attractivity and periodic nature of the solutions of the difference equations x_{n+1}=ax_{n-1}±((bx_{n-1}x_{n-2})/(cx_{n-2}±dx_{n-4})),    n=0,1,2,..., where the initial conditions x₋₄, x₋₃ ,x₋₂, x₋₁ and x₀ are arbitrary positive real numbers and a, b, c, d are constants

Asymptotically polynomial solutions of difference equations of neutral type

Asymptotic properties of solutions of difference equation of the form $$\Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n$$ are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or all nonoscillatory solutions are asymptotically polynomial. We use a new technique which allows us to control the degree of approximation

The Dynamics and Attractivity for a Rational Recursive Sequence of Order Three

This paper is concerned with the behavior of solution of the nonlinear difference equation where the initial conditions are arbitrary positive real numbers and a,b,c,d,e are positive constants

On the Solutions of a General System of Difference Equations

We deal with the solutions of the systems of the difference equations xn+1=1/xn-pyn-p, yn+1=xn-pyn-p/xn-qyn-q, and xn+1=1/xn-pyn-pzn-p, yn+1=xn-pyn-pzn-p/xn-qyn-qzn-q, zn+1=xn-qyn-qzn-q/xn-ryn-rzn-r, with a nonzero real numbers initial conditions. Also, the periodicity of the general system of k variables will be considered

Local dynamics and global attractivity of a certain second-order quadratic fractional difference equation

We investigate the local and global character of the equilibrium and the local stability of the period-two solution of the difference equation [Mathematical equations cannot be displayed here, refer to PDF] where the parameters β, γ, δ, B, C, D are nonnegative numbers which satisfy B + C + D \u3e 0 and the initial conditions x-1 and x0 are arbitrary nonnegative numbers such that Bxnxn-1 + Cx2n-1 + Dxn \u3e 0 for all n ≥ 0

Basin of attraction of triangular maps with applications

We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasi-homogeneous maps, and some multiplicative and additive difference equations, as well.Comment: 1 figur