Abstract
We investigate behavior of solutions of the following systems of rational difference equations: xn+1=yn-3k-1/(±1±yn-(3k-1)xn-(2k-1)yn-(k-1)),yn+1=xn-3k-1/(±1±xn-3k-1yn-2k-1xn-k-1), where k is a positive integer and the initial conditions are real numbers. We show that every solution is periodic with 6k period, considerably improving the results in the literature.
Highlights
A great effort has been made in studying qualitative properties of the solutions of systems of rational difference equations
Kurbanli et al [2] studied the behavior of positive solutions of the following system: xn+1
Elsayed [3, 4] obtained the solutions of the following systems of difference equations: xn+1
Summary
Cinar [1] studied periodicity of the positive solutions of the system of difference equations xn+1 Elsayed [3, 4] obtained the solutions of the following systems of difference equations: xn+1 Touafek and Elsayed [5] investigated the periodic nature and form of the solutions of the following systems of rational difference equations: xn+1
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