{"id":"W2153641542","doi":"10.1142/s0218127414500837","title":"Seven Limit Cycles Around a Focus Point in a Simple Three-Dimensional Quadratic Vector Field","year":2014,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Center manifold; Vector field; Focus (optics); Quadratic equation; Limit (mathematics); Manifold (fluid mechanics); Computation; Field (mathematics); Polynomial; Applied mathematics; Mathematical analysis; Pure mathematics; Geometry; Hopf bifurcation; Algorithm; Physics; Bifurcation","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0003008581,0.00009776343,0.0001983472,0.0001749577,0.00003550901,0.00005350399,0.0001474014,0.00005927197,0.00006606505],"category_scores_gemma":[0.000577202,0.00007901294,0.00007243626,0.00006862565,0.00002192547,0.0001883502,0.00003515472,0.0001372941,0.000005746472],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006769774,"about_ca_system_score_gemma":0.00003234914,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009758889,"about_ca_topic_score_gemma":0.0006280495,"domain_scores_codex":[0.998827,0.0000580588,0.0005447124,0.000106695,0.0003639559,0.00009960264],"domain_scores_gemma":[0.9986883,0.0005623801,0.0003534006,0.00008564778,0.000240498,0.00006971802],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0008268672,0.001649955,0.02522868,0.0001417704,0.0004818265,0.00005170014,0.002745731,0.001957279,0.007890564,0.7159571,0.001230056,0.2418385],"study_design_scores_gemma":[0.002156015,0.0003228815,0.01655716,0.0003082517,0.00003494417,0.0001541578,0.0003040122,0.1016242,0.0006860556,0.8766444,0.0009674463,0.0002404922],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.765411,0.00006728641,0.2297762,0.004067799,0.0003258405,0.0001115709,0.000004732795,0.00001096067,0.0002245994],"genre_scores_gemma":[0.996841,0.000009015061,0.002621956,0.0001764582,0.000292184,0.000006516328,0.000003944755,0.000009362789,0.0000395779],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.241598,"threshold_uncertainty_score":0.3222054,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02436612377960034,"score_gpt":0.3099338730791348,"score_spread":0.2855677492995344,"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."}}