Qualitative Properties of Difference Equation of Order Six

Abstract

Abstract:In this paper we study the qualitative properties and the periodic nature of the solutions of the difference equationwhere the initial conditions x −5 , x −4 , x −3 , x −2 , x −1 , x 0 are arbitrary positive real numbers and α, β, γ, δ are positive constants. In addition, we derive the form of the solutions of some special cases of this equation.

On the solutions of a second-order difference equation in terms of generalized Padovan sequences

“…Recently, the problem of finding closed-form solutions of rational difference equations and systems of rational of difference equations have gained considerable interest from many mathematicians. In fact, countless papers have been published previously focusing on the aforementioned topic, see for example [5,6,7,16,20] and [21]. Interestingly, some of the solution forms of these equations are even expressible in terms of well-known integer sequences such as the Fibonacci numbers, Horadam numbers and Padovan numbers (see, e.g., [9,11,12,14,22,24,25,26,27,29,34]).…”

Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

“…Proof. From ( 16), we see that the function g(v, w), which defined in (15), is increasing in v and decreasing in w. Let (ρ, τ) be a solution of the system:…”

“…Khaliq and Elsayed [15] examined the dynamics behavior and existence of the periodic solution of the difference equation:…”

On the dynamical behaviors of a quadratic difference equation of order three

“…The second approach is to obtain the solution's expressions if it is feasible since there are insufficient and explicit methods to find the solution of nonlinear difference equation. Khaliq and Elsayed [24] studied the dynamics behavior and existence of the periodic solution of the difference equation:…”