On the Dynamics of the Higher Order Nonlinear Rational Difference Equation

On the Dynamics of the Higher Order Nonlinear Rational Difference Equation

In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equation xn+1 = Axn +Bxn−k +Cxn−l +Dxn−σ + bxn−k [dxn−k − exn−l ] , n = 0,1,2, ....., where the coefficients A,B,C,D,b,d,e ∈ (0,∞), while k, l and σ are positive integers. The initial conditions x−σ ,...,x−l ,...,x−k, ...,x−1,x0 are arbitrary positi...

Dynamics of a System of Rational Higher-Order Difference Equation

Dynamics and behavior of a higher order rational difference equation

We study the global result, boundedness, and periodicity of solutions of the difference equation xn+1 = a+ bxn−l + cxn−k dxn−l + exn−k , n = 0, 1, . . . , where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x−t, x−t+1, . . . , x−1 and x0 are positive real numbers where t = max{l, k}, l 6= k. c ©2016 All rights reserved.

Dynamics of a higher-order rational difference equation

Global Dynamics for a Higher Order Rational Difference Equation

In this paper, some properties of all positive solutions are considered for a higher order rational difference equation, mainly for the existence of eventual prime period two solutions, the existence and asymptotic behavior of nonoscillatory solutions and the global asymptotic stability of its equilibria. Our results show that a positive equilibrium point of this equation is a global attractor ...