Dynamics and Solutions of Higher-Order Difference Equations

Mensah Folly-Gbetoula ()
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Mensah Folly-Gbetoula: School of Mathematics, University of the Witwatersrand, Johannesburg 2000, South Africa

Mathematics, 2023, vol. 11, issue 17, 1-16

Abstract: The invariance method, known as Lie analysis, consists of finding a group of transformations that leave a difference equation invariant. This powerful tool permits one to lower the order, linearize and more importantly, obtain analytical solutions of difference and differential equations. In this study, we obtain the solutions and periodic solutions for some family of difference equations. We achieve this by performing an invariance analysis of this family. Eventually, symmetries are derived and used to construct canonical coordinates required for the derivation of the solutions. Moreover, periodic aspects of these solutions and the stability character of the equilibrium points are investigated.

Keywords: difference equation; symmetry; periodicity; exact solution; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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