{"paper":{"title":"Symmetry induced Dynamics in four-dimensional Models deriving from the van der Pol Equation","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.CD","authors_text":"Ricardo Lopez-Ruiz","submitted_at":"2003-09-04T14:32:05Z","abstract_excerpt":"Different models of self-excited oscillators which are four-dimensional extensions of the van der Pol system are reported. Their symmetries are analyzed. Three of them were introduced to model the release of vortices behind circular cylinders with a possible transition from a symmetric to an antisymmetric Benard-von Karman vortex street. The fourth reported self-excited oscillator is a new model which implements the breaking of the inversion symmetry. It presents the phenomenon of second harmonic generation in a natural way. The parallelism with second harmonic generation in nonlinear optics i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0309013","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"}