{"id":"W4392736773","doi":"10.48550/arxiv.2403.05744","title":"Bi-center conditions and bifurcation of limit cycles in a class of $Z_2$-equivariant cubic switching systems with two nilpotent points","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Basic and Applied Basic Research Foundation of Guangdong Province; China Postdoctoral Science Foundation; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Nilpotent; Equivariant map; Bifurcation; Center (category theory); Mathematics; Limit (mathematics); Class (philosophy); Pure mathematics; Mathematical analysis; Physics; Computer science; Nonlinear system; Quantum mechanics; Chemistry; Crystallography","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000195213,0.0002396987,0.000544501,0.0004220196,0.00004673052,0.00003226216,0.000187736,0.0001629075,0.000007513197],"category_scores_gemma":[0.00004920334,0.0002158847,0.0001084676,0.0003357871,0.00009889855,0.00009471555,0.0003710366,0.0003408236,0.000003907222],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000164365,"about_ca_system_score_gemma":0.00008055871,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005708726,"about_ca_topic_score_gemma":0.0003877848,"domain_scores_codex":[0.998595,0.0001345728,0.0004850128,0.0004873382,0.0001160911,0.0001820035],"domain_scores_gemma":[0.9986221,0.0002374792,0.0004930963,0.0004277855,0.000141292,0.00007827314],"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":[0.0001085242,0.0004870068,0.005766221,0.002869699,0.0003010283,0.00005985169,0.00070182,0.08237869,0.001145755,0.9060914,0.000007916622,0.00008208188],"study_design_scores_gemma":[0.001582367,0.00009868268,0.001453073,0.004115428,0.0003781781,0.00001229834,0.00101505,0.5658496,0.00008639994,0.4250397,0.000007636015,0.000361587],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8331773,0.00006533378,0.1652794,0.00003070775,0.0001668381,0.0005599993,0.0001264473,0.00004040764,0.0005536189],"genre_scores_gemma":[0.9991724,0.00004851175,0.0005138144,0.000002985346,0.00002570888,0.000005203154,0.0000461285,0.00002842615,0.0001567589],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4834709,"threshold_uncertainty_score":0.8803522,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0797936216078164,"score_gpt":0.2431864383293166,"score_spread":0.1633928167215001,"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."}}