{"id":"W2951545641","doi":"10.48550/arxiv.math/0505392","title":"Toroidal normal forms for bifurcations in retarded functional differential equations I: Multiple Hopf and transcritical/multiple Hopf interaction","year":2005,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Hopf bifurcation; Mathematics; Pitchfork bifurcation; Nonlinear system; Differential equation; Realizability; Mathematical analysis; Applied mathematics; Bifurcation; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001892659,0.0004698317,0.0006430845,0.0002879051,0.0003440454,0.000107292,0.00020686,0.0004913908,0.0001939013],"category_scores_gemma":[0.001373448,0.0004469647,0.0003429576,0.0001524936,0.0001144813,0.0003928171,0.0001821031,0.0007199722,0.0000208156],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003296741,"about_ca_system_score_gemma":0.00009521147,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001886266,"about_ca_topic_score_gemma":0.003931415,"domain_scores_codex":[0.9971812,0.0001035648,0.001111707,0.0007423568,0.0003513634,0.0005098562],"domain_scores_gemma":[0.9971171,0.001627634,0.0003035025,0.0004980218,0.0002597995,0.0001939434],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.006038782,0.01424929,0.5804261,0.008317388,0.002368915,0.00002055314,0.01025003,0.03615624,0.1216997,0.1970626,0.001004477,0.02240593],"study_design_scores_gemma":[0.01114125,0.0002706667,0.3647074,0.0008201825,0.0006560406,0.00001925345,0.001113689,0.5567259,0.001649826,0.05985812,0.00101132,0.002026308],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5745914,0.00004922091,0.4229072,0.0003059509,0.000573526,0.001090859,0.0003125094,0.00009807591,0.00007131744],"genre_scores_gemma":[0.9913539,0.00003414421,0.004658144,0.00003081078,0.0006728679,0.00121567,0.001349427,0.00007619033,0.0006088619],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5205697,"threshold_uncertainty_score":0.9997982,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1094675266622763,"score_gpt":0.3318996560977322,"score_spread":0.2224321294354559,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}