{"id":"W2038403487","doi":"10.1098/rspa.2006.1724","title":"Neimark–Sacker bifurcations in a non-standard numerical scheme for a class of positivity-preserving ODEs","year":2006,"lang":"en","type":"article","venue":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","topic":"Nonlinear Dynamics and Pattern Formation","field":"Computer Science","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"National Research Council Canada; National Research Council Institute for Biodiagnostics","funders":"","keywords":"Mathematics; Ode; Hopf bifurcation; Mathematical analysis; Ordinary differential equation; Bifurcation; Pitchfork bifurcation; Saddle-node bifurcation; Bifurcation theory; Bifurcation diagram; Lyapunov exponent; Type (biology); Applied mathematics; Differential equation; Nonlinear system; Physics","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":[0.0003122256,0.00008644427,0.0001826839,0.00002376661,0.00008130272,0.00007102687,0.0004029083,0.00003021113,4.050703e-7],"category_scores_gemma":[0.00005527029,0.00005835701,0.0001184393,0.0003689321,0.0001160289,0.0002526653,0.0001918488,0.00008107598,2.154195e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000157798,"about_ca_system_score_gemma":0.0000135748,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001273676,"about_ca_topic_score_gemma":2.627187e-7,"domain_scores_codex":[0.9992512,0.000001971744,0.0001932669,0.0001500551,0.0002339362,0.0001695446],"domain_scores_gemma":[0.9996234,0.0001387243,0.00008383536,0.00005919994,0.00006799208,0.00002684683],"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":[0.000009792948,0.0004512999,0.003524081,0.001663604,0.00002975443,4.470416e-8,0.003311028,0.01462688,0.03762053,0.9378576,0.000209913,0.0006955073],"study_design_scores_gemma":[0.0001120337,0.00004603108,0.00459883,0.0001195,0.00000476651,4.310353e-7,0.00004188094,0.9457083,0.002126774,0.04716556,0.000006467181,0.00006944053],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7885227,0.00001002687,0.2103916,0.0005335036,0.00001704848,0.0001378614,0.000004889472,0.00001585454,0.0003666148],"genre_scores_gemma":[0.9069567,5.747439e-7,0.09297261,0.00001203811,0.00002773597,0.00001432979,2.427751e-7,0.00000344202,0.00001232329],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9310814,"threshold_uncertainty_score":0.237973,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006107256178587626,"score_gpt":0.2170469237204069,"score_spread":0.2109396675418193,"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."}}