{"id":"W2129845849","doi":"10.1142/s021812741002791x","title":"THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE","year":2010,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Phase portrait; Mathematics; Invariant theory; Bifurcation diagram; Quadratic differential; Invariant (physics); Infinite-period bifurcation; Mathematical analysis; Pure mathematics; Bifurcation; Quadratic equation; Discrete mathematics; Geometry; Algebra over a field; Physics; Quantum mechanics; Mathematical 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":[],"consensus_categories":[],"category_scores_codex":[0.0002570697,0.00009827053,0.0001925296,0.0001237674,0.00008038234,0.0001250288,0.0001787657,0.00005925284,0.00002294595],"category_scores_gemma":[0.0001508694,0.00005604854,0.00003685263,0.00005898874,0.0001054094,0.0001905563,0.0000273082,0.0001812373,3.598008e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001606821,"about_ca_system_score_gemma":0.00004845286,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005311042,"about_ca_topic_score_gemma":0.0002647832,"domain_scores_codex":[0.9988565,0.00005245193,0.0005311628,0.00009247048,0.0003835045,0.00008394905],"domain_scores_gemma":[0.9985268,0.0002648116,0.000608298,0.0001108728,0.0003961348,0.0000930639],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001086419,0.0009110965,0.003239936,0.0001274339,0.0007291251,0.00001293891,0.001792546,0.0001091256,0.08410659,0.8563704,0.0001223282,0.05139198],"study_design_scores_gemma":[0.04213583,0.01018012,0.1159372,0.003163904,0.001795666,0.006823484,0.01961318,0.4833682,0.02328715,0.279644,0.01083212,0.003219218],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9049534,0.00009055251,0.09340996,0.0005999096,0.0006574874,0.0001404411,0.0000168103,0.000006281377,0.0001251547],"genre_scores_gemma":[0.9983326,0.00004572685,0.0009899777,0.000006303047,0.0004849712,0.000004914654,0.000004329749,0.000009621341,0.0001215306],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5767265,"threshold_uncertainty_score":0.2285593,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01578043234384222,"score_gpt":0.3005627682972236,"score_spread":0.2847823359533814,"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."}}