{"paper":{"title":"Qualitative analysis of certain generalized classes of quadratic oscillator systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.CD"],"primary_cat":"math-ph","authors_text":"Barnali Pal, Bijan Bagchi, Samiran Ghosh, Swarup Poria","submitted_at":"2015-11-06T12:49:32Z","abstract_excerpt":"We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by C. Quesne [J.Math.Phys.\\textbf{56},012903 (2015)]. By performing a local analysis of the governing potentials we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength $\\lambda$, the other points to a centre for $\\lambda < 0$ but a saddle $\\lambda > 0$. On the other hand, the second potential reveals only a center for both the signs of $\\lambda$ from a linear stability analy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02054","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"}