{"id":"W2087291239","doi":"10.1016/j.nonrwa.2010.12.012","title":"Phase portraits, Hopf bifurcations and limit cycles of the Holling–Tanner models for predator–prey interactions","year":2010,"lang":"en","type":"article","venue":"Nonlinear Analysis Real World Applications","topic":"Mathematical and Theoretical Epidemiology and Ecology Models","field":"Medicine","cited_by":40,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Phase portrait; Uniqueness; Hopf bifurcation; Limit (mathematics); Mathematics; Predation; Lyapunov function; Applied mathematics; Limit cycle; Stability (learning theory); Mathematical analysis; Statistical physics; Bifurcation; Physics; Ecology; Computer science; Nonlinear system; Biology","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":[0.0002112533,0.0002692419,0.0002781556,0.000618192,0.0003284797,0.000580353,0.0003369779,0.0005942128,0.003603124],"category_scores_gemma":[0.0008912252,0.0002096337,0.0003811976,0.000261918,0.0005172998,0.0006598451,0.0003142354,0.0003843208,0.0003019117],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005013647,"about_ca_system_score_gemma":0.0001868221,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001796503,"about_ca_topic_score_gemma":0.001377603,"domain_scores_codex":[0.9999483,0.00002314577,0.000002307325,0.000007289907,0.00001166471,0.000007302507],"domain_scores_gemma":[0.9998031,0.00009831166,0.00004339962,0.0000165949,0.00001940818,0.00001921862],"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":[0.0001811833,0.00006874386,0.004750405,0.0001827145,0.0001207823,0.0004863709,0.001009136,0.2868136,0.02432111,0.6452534,0.005906637,0.03090587],"study_design_scores_gemma":[0.00003252995,0.00002948794,0.003258365,0.00001829232,0.00002525402,0.0002661376,0.0001394839,0.7195919,0.001239549,0.2724299,0.002943313,0.00002601213],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8092692,0.001770371,0.1436312,0.001138372,0.00007385793,0.00006725765,0.0003755164,0.0002369644,0.04343721],"genre_scores_gemma":[0.990657,0.0003834254,0.004129987,0.00004172892,0.00001619433,0.00003240999,0.00007937508,0.00001944252,0.004640466],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003603124,"threshold_uncertainty_score":0.01205367,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03200602686133564,"score_gpt":0.3564169696139118,"score_spread":0.3244109427525762,"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."}}