Some General Systems of Rational Difference Equations. (5th March 2015) - Gelisken, Ali; Kara, Merve
Abstract : We investigate behavior of solutions of the following systems of rational difference equations:x n + 1 = y n - 3 k - 1 / ( ± 1 ± y n - ( 3 k - 1 ) x n - ( 2 k - 1 ) y n - ( k - 1 ) ), y n + 1 = x n - 3 k - 1 / ( ± 1 ± x n - 3 k - 1 y n - 2 k - 1 x n - k - 1 ), wherek is a positive integer and the initial conditions are real numbers. We show that every solution is periodic with6 k period, considerably improving the results in the literature.