Dynamics of the third order Lyness' difference equation

Dynamics of the Third Order Lyness’ Difference Equation

This paper studies the iterates of the third order Lyness’ recurrence xk+3 = (a + xk+1 + xk+2)/xk, with positive initial conditions, being a also a positive parameter. It is known that for a = 1 all the sequences generated by this recurrence are 8-periodic. We prove that for each a 6= 1 there are infinitely many initial conditions giving rise to periodic sequences which have almost all the even...

On a k-Order System of Lyness-Type Difference Equations

We consider the following system of Lyness-type difference equations: x1(n + 1) = (akxk(n) + bk)/xk−1(n − 1), x2(n + 1) = (a1x1(n) + b1)/xk(n − 1), xi(n + 1) = (ai−1xi−1(n) + bi−1)/xi−2(n− 1), i= 3,4, . . . ,k, where ai, bi, i= 1,2, . . . ,k, are positive constants, k ≥ 3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the ...

On the Dynamics of a Higher-Order Difference Equation

This paper deals with the investigation of the following more general rational difference equation: yn 1 αyn/ β γ ∑k i 0 y p n− 2i 1 ∏k i 0yn− 2i 1 , n 0, 1, 2, . . . ,where α, β, γ, p ∈ 0,∞ with the initial conditions x0, x−1, . . . , x−2k, x−2k−1 ∈ 0,∞ . We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, som...

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.