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Journal of Applied Nonlinear Dynamics 14(2) (2025) 483--498 | DOI:10.5890/JAND.2025.06.015

Kgatliso Mkhwanazi, Mensah Folly-Gbetoula

School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

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Abstract

In this paper, we use the invariance method to obtain symmetries and exact solutions for a class of difference equations with variable coefficients. We look at the stability of the equilibrium points admitted by this class. Behavior and periodicity of their solutions are investigated. Consequently, results in existing literature [Elsayed, E.M., Alofi, B. S. and Khan,A. Q. (2022), Qualitative behavior of solutions of tenth-order recursive sequence equation, \textit{Mathematical Problems in Engineering}, ID 5242325] are generalized.

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