{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T00:33:48Z","timestamp":1761352428415,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T00:00:00Z","timestamp":1671408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Funding (NRF) of South Africa","doi-asserted-by":"publisher","award":["132108"],"award-info":[{"award-number":["132108"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give sufficient conditions for the existence of two-periodic and four-periodic solutions in certain cases. Our results generalize and simplify some work in the literature.<\/jats:p>","DOI":"10.3390\/sym14122683","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T06:58:29Z","timestamp":1671433109000},"page":"2683","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Simplification and Generalization of Elsayed and Ibrahim\u2019s Two-Dimensional System of Third-Order Difference Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3046-0679","authenticated-orcid":false,"given":"Mensah","family":"Folly-Gbetoula","sequence":"first","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa"}]},{"given":"Darlison","family":"Nyirenda","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,19]]},"reference":[{"key":"ref_1","first-page":"33","article-title":"The Solution and Dynamic Behavior of Some Difference Equations of Fourth Order","volume":"29","author":"Almatrafi","year":"2022","journal-title":"Discret. 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Equ."},{"key":"ref_16","first-page":"2350063","article-title":"Triki\u2013Biswas model: Its symmetry reduction, Nucci\u2019s reduction and conservation laws","volume":"2022","author":"Akbulut","year":"2022","journal-title":"Int. J. Mod. Phys B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s40314-022-01977-1","article-title":"Analytical treatment of regularized Prabhakar fractional differential equations by invariant subspaces","volume":"41","author":"Chu","year":"2022","journal-title":"Comput. Appl. Math."},{"key":"ref_18","first-page":"1361","article-title":"Periodicity and solutions for some systems of nonlinear rational difference equations","volume":"44","author":"Elsayed","year":"2015","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Olver, P.J. (1993). Applications of Lie Groups to Differential Equations, Springer. 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