{"paper":{"title":"A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"physics.comp-ph","authors_text":"Bulcs\\'u S\\'andor, Claudius Gros","submitted_at":"2015-04-13T13:16:10Z","abstract_excerpt":"We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and transitions to chaos induced by sequences of limit cycle bifurcations. The prototype system consist of a $2d$-dimensional dynamical system with friction forces $f(V(\\mathbf{x}))$ functionally dependent exclusively on the mechanical potential $V(\\mathbf{x})$, which is typically characterized, here, by a finite number of local minima. We present examples for $d=1,2$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03167","kind":"arxiv","version":1},"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"}