{"id":"W1960050943","doi":"10.1016/j.jde.2015.09.016","title":"Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials","year":2015,"lang":"en","type":"article","venue":"Journal of Differential Equations","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Bifurcation; Quadratic equation; Amplitude; Limit (mathematics); Hamiltonian (control theory); Mathematical analysis; Limit cycle; Singular point of a curve; Cubic function; Computation; Vector field; Infinite-period bifurcation; Bifurcation theory; Geometry; Physics; 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":[0.0003384975,0.0003257642,0.0004420592,0.0007612903,0.001256184,0.0008683723,0.0005836939,0.0008977563,0.004268054],"category_scores_gemma":[0.00115633,0.0002583195,0.0004328258,0.0002954446,0.001228654,0.0005500045,0.0009383775,0.0004948086,0.0001899171],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008776605,"about_ca_system_score_gemma":0.0004533008,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001254188,"about_ca_topic_score_gemma":0.001319087,"domain_scores_codex":[0.9998804,0.00002498776,0.000006644153,0.00001820052,0.00003526848,0.00003446644],"domain_scores_gemma":[0.9996783,0.00008162465,0.00004816636,0.00003665166,0.00004153776,0.0001136998],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001630876,0.0008678344,0.01577171,0.000443826,0.0004211668,0.00521861,0.003888827,0.3754317,0.2014705,0.3499633,0.003989856,0.04090183],"study_design_scores_gemma":[0.0001149145,0.0004655632,0.007704757,0.00004294496,0.0000687816,0.000458018,0.0008780835,0.9007883,0.01510648,0.07192059,0.002377165,0.0000744355],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.984148,0.00004930747,0.006086144,0.0001654353,0.00004002118,0.00003625045,0.00002690161,0.00005695886,0.009391006],"genre_scores_gemma":[0.9973781,0.00001689708,0.001241483,0.00002102141,0.0000043625,0.00001373241,0.00002070018,0.00001373885,0.001289925],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004268054,"threshold_uncertainty_score":0.01427805,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06543773984126545,"score_gpt":0.2985288666492339,"score_spread":0.2330911268079685,"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."}}