Analytical Study of the Difference Equation `x_{n+1}=\dfrac{x_{n} x_{n-6}}{x_{n-5}\left(\pm 1 - x_nx_{n-6}\right)}`
Abdualrazaq Sanbo *
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia. and Department of General Studies, Jeddah College of Telecom and Electronics, TVTC, B.P. 2816, Jeddah 21461, Saudi Arabia.
Elsayed M. Elsayed
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia. and Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Faris Alzahrani
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
This paper is devoted to find the form of the solutions of a rational difference equations with arbitrary positive real initial conditions. Specific form of the solutions of two special cases of this equation are given.
Keywords: Difference equations, Recursive sequences, Stability, Boundedness.