{"paper":{"title":"Solution Form of a Higher Order System of Difference Equation and Dynamical Behavior of Its Special Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Julius Fergy T. Rabago, Nabila Haddad, Nouressadat Touafek","submitted_at":"2016-01-09T05:45:00Z","abstract_excerpt":"The solution form of the system of nonlinear difference equations \\begin{equation*} x_{n+1} = \\frac{x_{n-k+1}^{p}y_{n}}{a y_{n-k}^{p}+b y_{n}},\\ y_{n+1} = \\frac{y_{n-k+1}^{p}x_{n}}{\\alpha x_{n-k}^{p}+\\beta x_{n}}, \\quad n, p \\in \\mathbb{N}_{0},\\ k\\in \\mathbb{N}, \\end{equation*} where the coefficients $a, b, \\alpha, \\beta$ and the initial values $x_{-i},y_{-i},i\\in\\{0,1,\\ldots,k\\}$ are real numbers, is obtained. Furthermore, the behavior of solutions of the above system when $p=1$ is examined. Numerical examples are presented to illustrate the results exhibited in the paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02078","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}