{"id":"W2169781449","doi":"10.1142/s0218127407018300","title":"LIMIT CYCLES IN TWO TYPES OF SYMMETRIC LIÉNARD SYSTEMS","year":2007,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Limit (mathematics); Mathematics; Singularity; Limit cycle; Polynomial; Nonlinear system; Liénard equation; Hopf bifurcation; Mathematical analysis; Pure mathematics; Physics; Bifurcation; Quantum mechanics; Differential equation","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":[0.0005122331,0.00006454138,0.000182091,0.000467316,0.00001350172,0.00002233354,0.000131742,0.00003382443,0.00001161863],"category_scores_gemma":[0.0003032385,0.00005239954,0.00005045557,0.0001663329,0.00002533448,0.0001231576,0.0000198456,0.00008610966,0.000001784492],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006360779,"about_ca_system_score_gemma":0.00002172577,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000065907,"about_ca_topic_score_gemma":0.00006898116,"domain_scores_codex":[0.9988205,0.00003081977,0.0006601144,0.00006442046,0.0003483779,0.00007577311],"domain_scores_gemma":[0.9986377,0.0003297107,0.0005162352,0.00005755219,0.0004103275,0.00004842786],"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":[0.0002589063,0.0005996157,0.03183211,0.0001184407,0.0002101185,0.00002707262,0.001027174,0.0008664895,0.005275425,0.8942509,0.00007204559,0.0654617],"study_design_scores_gemma":[0.017224,0.001070663,0.2966345,0.004048468,0.0003095625,0.001227465,0.008612226,0.09575287,0.01083537,0.5547343,0.008217988,0.001332633],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8970095,0.0004463047,0.1003437,0.0002403885,0.0006902433,0.0001006894,0.000005716039,0.000006637577,0.001156821],"genre_scores_gemma":[0.9981655,0.00009018966,0.001425726,0.0000149888,0.00019439,0.000001233877,0.00000223972,0.00000646991,0.00009926262],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3395166,"threshold_uncertainty_score":0.2136791,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03645210477501562,"score_gpt":0.3761083598889664,"score_spread":0.3396562551139508,"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."}}