{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T04:15:02Z","timestamp":1769919302650,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T00:00:00Z","timestamp":1669075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["RGP.2\/47\/43\/1443"],"award-info":[{"award-number":["RGP.2\/47\/43\/1443"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We examine the unboundedness, persistence, boundedness, uniqueness, and existence of non-negative equilibrium of an exponential symmetric difference equations system: \u03a9n+1=\u03b11+\u03b21\u03a9n+\u03b31\u03a9n\u22121e\u2212(\u03a9n+\u03d6n), \u03d6n+1=\u03b12+\u03b22\u03d6n+\u03b32\u03d6n\u22121e\u2212(\u03a9n+\u03d6n),n=0,1,\u22ef, whereby initial values \u03a9\u22121,\u03d6\u22121,\u03a90,\u03d60 and parameters \u03b11,\u03b12 are non-negative real numbers and \u03b21,\u03b22\u2208(0,1) and \u03b31,\u03b32\u22640. We will discuss asymptotic global and local stability and the convergence rate of this system. Ultimately, to check our results, we set out some numerical explanations.<\/jats:p>","DOI":"10.3390\/sym14122474","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T08:27:29Z","timestamp":1669105649000},"page":"2474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Qualitative Behavior of an Exponential Symmetric Difference Equation System"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6895-3268","authenticated-orcid":false,"given":"Tarek F.","family":"Ibrahim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha 62529, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Sciences, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6836-8803","authenticated-orcid":false,"given":"Somayah","family":"Refaei","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Jazan University, Jazan 82511, Saudi Arabia"}]},{"given":"Abdul","family":"Khaliq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1676-2662","authenticated-orcid":false,"given":"Mohamed Abd","family":"El-Moneam","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Jazan University, Jazan 82511, Saudi Arabia"}]},{"given":"Bakri A.","family":"Younis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts in Elmagarda, King Khalid University, Abha 62529, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3465-0947","authenticated-orcid":false,"given":"Waleed M.","family":"Osman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, King Khalid University, Abha 62529, Saudi Arabia"}]},{"given":"Bushra R.","family":"Al-Sinan","sequence":"additional","affiliation":[{"name":"Department of Administrative and Financial Sciences, Nairiyah College, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P. 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