Dynamics and behavior of a higher order rational 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.

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

Global Behavior of a Higher-order Rational Difference Equation

We investigate in this paper the global behavior of the following difference equation: xn+1 = (Pk(xn i0 ,xn i1 , . . . ,xn i2k ) + b)/(Qk(xn i0 ,xn i1 , . . . ,xn i2k ) + b), n = 0,1, . . ., under appropriate assumptions, where b [0, ), k 1, i0, i1, . . . , i2k 0,1, . . . with i0 < i1 < < i2k, the initial conditions xi 2k ,xi 2k+1, . . . ,x0 (0, ). We prove that unique equilibrium x = 1 of that...

Dynamics of a System of Rational Higher-Order Difference Equation

Dynamics of a higher-order rational difference equation