General form of the solutions of some difference equations via Lie symmetry analysis

2019/10/15 by Mensah Folly-Gbetoula, Folly-Gbetoula, Mensah, Melih Göcen +3
Mathematics · Medicine · Physics and Astronomy · #39A10 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1910.06880

openalex publication_date 2019/10/15 · openalex created_date 2019/10/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain exact solutions of the following rational difference equation x_n+1=\fracx_nx_n-2x_n-4 x_n-1x_n-3(a_n+b_nx_nx_n-2x_n-4), where a_n and b_n 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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