{"id":"W1682979569","doi":"10.1007/s00332-015-9266-5","title":"A Degenerate Hopf Bifurcation in Retarded Functional Differential Equations, and Applications to Endemic Bubbles","year":2015,"lang":"en","type":"article","venue":"Journal of Nonlinear Science","topic":"Mathematical and Theoretical Epidemiology and Ecology Models","field":"Medicine","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Hopf bifurcation; Mathematics; Degenerate energy levels; Center manifold; Pitchfork bifurcation; Saddle-node bifurcation; Biological applications of bifurcation theory; Transcritical bifurcation; Eigenvalues and eigenvectors; Bifurcation diagram; Mathematical analysis; Bogdanov–Takens bifurcation; Codimension; Bifurcation; Physics; Nonlinear system","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":[0.001719159,0.0006446842,0.001039933,0.002079551,0.001159029,0.001914737,0.0008501573,0.0021757,0.003251887],"category_scores_gemma":[0.009757828,0.0004133484,0.001318382,0.0008513928,0.002487162,0.002813782,0.002799726,0.00132618,0.000195486],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009653958,"about_ca_system_score_gemma":0.0007989347,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001853034,"about_ca_topic_score_gemma":0.001130833,"domain_scores_codex":[0.9997471,0.0001200803,0.00001857275,0.00004076649,0.00004398746,0.00002949983],"domain_scores_gemma":[0.9980178,0.001154536,0.0002538129,0.00007451035,0.0002363115,0.0002630904],"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":[0.00006452462,0.00004365346,0.001150628,0.0001485228,0.00003737117,0.0005020898,0.0003387503,0.0330847,0.003210921,0.9522354,0.001635316,0.007548067],"study_design_scores_gemma":[0.00003837648,0.00004842006,0.0004748754,0.0000406922,0.0000336051,0.0004172288,0.0001713302,0.323548,0.0003546732,0.6726604,0.002176051,0.00003645275],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3378747,0.008507987,0.5862526,0.007573305,0.0009769524,0.0001365541,0.0001874355,0.0003195701,0.05817096],"genre_scores_gemma":[0.9504483,0.002529114,0.02971241,0.0004972423,0.0005450295,0.00008714834,0.00005794451,0.00005510537,0.01606776],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003251887,"threshold_uncertainty_score":0.01087862,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08460184411259103,"score_gpt":0.3428156071080934,"score_spread":0.2582137629955024,"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."}}