Period-Two Solutions to Some Systems of Rational Difference Equations

Abstract

We consider period-two solutions to various cases of the difference equations $$x_{n+1} = \frac{A+Bx_{n}+Cy_{n}} {D+Ex_{n}+Fy_{n}}$$ , $$y_{n+1} = \frac{J+Kx_{n}+Ly_{n}} {P+Qx_{n}+Ry_{n}}$$ . We give several examples of period-two solutions and in some cases categorize prime period-two solutions. We also apply our techniques to a single second-order rational difference equation to get circumstances leading to a prime period-two solution.