{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:34:49Z","timestamp":1753886089704,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,6,11]],"date-time":"2008-06-11T00:00:00Z","timestamp":1213142400000},"content-version":"vor","delay-in-days":162,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We study the global stability, the periodic character, and the boundedness character of the positive solutions of the difference equation <jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic>+1<\/jats:sub> = (<jats:italic>\u03b1<\/jats:italic> \u2212 <jats:italic>\u03b2<\/jats:italic><jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>)\/(<jats:italic>\u03b3<\/jats:italic> \u2212 <jats:italic>\u03b4<\/jats:italic><jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> \u2212 <jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic>\u2212<jats:italic>k<\/jats:italic><\/jats:sub>),\u2009\u2009<jats:italic>n<\/jats:italic> = 0, 1, 2, \u2026, \u2009\u2009<jats:italic>k<\/jats:italic> \u2208 {1, 2, \u2026}, in the two cases: (i) <jats:italic>\u03b4<\/jats:italic> \u2265 0, \u2009\u2009<jats:italic>\u03b1<\/jats:italic> &gt; 0, \u2009\u2009<jats:italic>\u03b3<\/jats:italic> &gt; <jats:italic>\u03b2<\/jats:italic> &gt; 0; (ii) <jats:italic>\u03b4<\/jats:italic> \u2265 0, \u2009\u2009<jats:italic>\u03b1<\/jats:italic> = 0, \u2009\u2009<jats:italic>\u03b3<\/jats:italic>, <jats:italic>\u03b2<\/jats:italic> &gt; 0, where the coefficients <jats:italic>\u03b1<\/jats:italic>, \u2009\u2009<jats:italic>\u03b2<\/jats:italic>, \u2009\u2009<jats:italic>\u03b3<\/jats:italic>, \u2009\u2009and\u2009\u2009<jats:italic>\u03b4<\/jats:italic>, and the initial conditions <jats:italic>x<\/jats:italic><jats:sub>\u2212<jats:italic>k<\/jats:italic><\/jats:sub>, <jats:italic>x<\/jats:italic><jats:sub>\u2212<jats:italic>k<\/jats:italic>+1<\/jats:sub>, \u2026, <jats:italic>x<\/jats:italic><jats:sub>\u22121<\/jats:sub>, <jats:italic>x<\/jats:italic><jats:sub>0<\/jats:sub> are real numbers. We show that the positive equilibrium of this equation is a global attractor with a basin that depends on certain conditions posed on the coefficients of this equation.<\/jats:p>","DOI":"10.1155\/2008\/391265","type":"journal-article","created":{"date-parts":[[2008,6,12]],"date-time":"2008-06-12T10:53:36Z","timestamp":1213268016000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Rational Recursive Sequence <i>x<\/i><sub><i>n<\/i>+1<\/sub> = (<i>\u03b1<\/i> \u2212 <i>\u03b2<\/i><i>x<\/i><sub><i>n<\/i><\/sub>)\/(<i>\u03b3<\/i> \u2212 <i>\u03b4<\/i><i>x<\/i><sub><i>n<\/i><\/sub> \u2212 <i>x<\/i><sub><i>n<\/i>\u2212<i>k<\/i><\/sub>)"],"prefix":"10.1155","volume":"2008","author":[{"given":"E. M. E.","family":"Zayed","sequence":"first","affiliation":[]},{"given":"A. B.","family":"Shamardan","sequence":"additional","affiliation":[]},{"given":"T. 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