{"id":"W2094167518","doi":"10.1142/s0218127407017252","title":"LOCAL AND GLOBAL BIFURCATIONS TO LIMIT CYCLES IN A CLASS OF LIÉNARD EQUATION","year":2007,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Limit (mathematics); Limit cycle; Liénard equation; Infinite-period bifurcation; Saddle point; Polynomial; Degree (music); Mathematical analysis; Function (biology); Saddle; Bifurcation; Phase space; Fixed point; Hopf bifurcation; Physics; Geometry; Differential equation; Nonlinear system; Mathematical optimization; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003028042,0.000352368,0.0006418769,0.0008670858,0.001056088,0.0008663686,0.0004672679,0.0008604956,0.001163655],"category_scores_gemma":[0.001174469,0.0002787758,0.000641469,0.0003096514,0.001403954,0.001012473,0.0009591047,0.0005329872,0.000110394],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007037974,"about_ca_system_score_gemma":0.0004300782,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003103114,"about_ca_topic_score_gemma":0.001614081,"domain_scores_codex":[0.9998757,0.00003399816,0.000006048964,0.00002437521,0.00003130087,0.00002853218],"domain_scores_gemma":[0.9997503,0.00007202537,0.00006485477,0.0000180363,0.0000358202,0.00005894415],"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":[0.0001486861,0.0001705301,0.01906001,0.0001920186,0.0002050945,0.0026892,0.001757008,0.4182211,0.01896906,0.5170356,0.002263531,0.01928821],"study_design_scores_gemma":[0.00003502289,0.00006544159,0.00243527,0.00001545218,0.00002514205,0.000375875,0.0002408795,0.8697712,0.00118283,0.1240317,0.001793287,0.00002784671],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9350705,0.000716746,0.05398691,0.0003250528,0.00003053551,0.0000397045,0.00002848911,0.0000637271,0.009738416],"genre_scores_gemma":[0.993501,0.000231792,0.004155466,0.00004196705,0.00002167973,0.00003552721,0.00003280626,0.0000176827,0.00196202],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003103114,"threshold_uncertainty_score":0.006170094,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04008030774284951,"score_gpt":0.3613236109413685,"score_spread":0.321243303198519,"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."}}