General form of the solutions of some difference equations via Lie symmetry analysis
Abstract
In this paper, we obtain exact solutions of the following rational difference equation xn+1=xnxn-2xn-4 xn-1xn-3(an+bnxnxn-2xn-4), where an and bn are random real sequences, by using the technique of Lie symmetry analysis. Moreover, we discuss the periodic nature and behavior of solutions for some special cases. This work is a generalization of some works by Elsayed and Ibrahim in [E.M.Elsayed, T. F. Ibrahim, Solutions and periodicity of a rational recursive sequences of order five, Bulletin of the Malaysian Mathematical Sciences Society 38:1 (2015), 95-112].
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