{"id":"W1995731991","doi":"10.1142/s0218127408022226","title":"LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER","year":2008,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":34,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Nilpotent; Mathematics; Bifurcation; Limit cycle; Infinite-period bifurcation; Saddle-node bifurcation; Transcritical bifurcation; Bifurcation diagram; Limit (mathematics); Hamiltonian system; Hamiltonian (control theory); Mathematical analysis; Hopf bifurcation; Bifurcation theory; Center (category theory); Pitchfork bifurcation; Pure mathematics; Physics; Nonlinear system; Quantum mechanics","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":[0.0001975139,0.0001199646,0.0002170589,0.0001986819,0.0001006037,0.00008008834,0.0002006415,0.0000682778,0.00002719529],"category_scores_gemma":[0.0001898363,0.0001016971,0.00007858897,0.0001204739,0.0000618527,0.0002726539,0.00003357648,0.000167144,0.000007152411],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000154519,"about_ca_system_score_gemma":0.00005626919,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009131676,"about_ca_topic_score_gemma":0.00002885919,"domain_scores_codex":[0.998516,0.00006652612,0.0006973857,0.0001341531,0.0004509712,0.0001349218],"domain_scores_gemma":[0.9988382,0.0001505509,0.0004275,0.0001048786,0.0003762644,0.0001025726],"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":[0.001493687,0.01472979,0.2825271,0.0006816945,0.002419194,0.0006407874,0.05156728,0.01655942,0.04119552,0.4516609,0.0258557,0.1106689],"study_design_scores_gemma":[0.02795244,0.001238551,0.1450615,0.003934185,0.0002566272,0.008663661,0.009283016,0.5655181,0.001361054,0.09154087,0.1422361,0.002953867],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9395056,0.0004615022,0.05627437,0.00206298,0.0008385998,0.000203796,0.00003102993,0.00002083711,0.0006013116],"genre_scores_gemma":[0.9976578,0.0002705625,0.001338049,0.0001011629,0.0001746463,0.00001296341,0.00001793986,0.00001474424,0.0004121076],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5489587,"threshold_uncertainty_score":0.4147088,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02988594203456894,"score_gpt":0.2955383401459565,"score_spread":0.2656523981113876,"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."}}