{"id":"W4387618993","doi":"10.1016/j.aml.2023.108894","title":"An analytical approach of applying the Lyapunov direct method to polynomial differential systems with discrete time delays","year":2023,"lang":"en","type":"article","venue":"Applied Mathematics Letters","topic":"Mathematical and Theoretical Epidemiology and Ecology Models","field":"Medicine","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Wilfrid Laurier University","funders":"Natural Science Basic Research Program of Shaanxi Province; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Lyapunov function; Positive definiteness; Polynomial; Applied mathematics; Boundary (topology); Lyapunov equation; Stability (learning theory); Equilibrium point; Control theory (sociology); Differential equation; Mathematical analysis; Nonlinear system; Positive-definite matrix; Computer science; Eigenvalues and eigenvectors; Control (management)","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00148707,0.0002647957,0.000982497,0.0001272331,0.0001362909,0.00001970611,0.000263963,0.0001590445,0.00009657187],"category_scores_gemma":[0.0001015294,0.0001396338,0.0001269339,0.0003582193,0.0003586006,0.00002631533,0.00009608793,0.0002847631,0.0001486819],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002169157,"about_ca_system_score_gemma":0.00002082595,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006969849,"about_ca_topic_score_gemma":2.161193e-7,"domain_scores_codex":[0.9981217,0.0001160165,0.0005889065,0.0003853843,0.0002982443,0.0004897068],"domain_scores_gemma":[0.9976485,0.001354668,0.0001415527,0.0005851255,0.00002989622,0.0002402107],"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":[0.0008959683,0.0007219698,0.00009650757,0.001460159,0.001029656,0.00002815307,0.001675708,0.008554532,0.04931632,0.9307443,0.004283233,0.001193426],"study_design_scores_gemma":[0.001030425,0.0002985227,0.0001891163,0.0001276786,0.0007968937,0.00007546088,0.0004811005,0.9906799,0.0010646,0.004746243,0.0001677419,0.0003422976],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.200335,0.000003906063,0.7804235,0.00158265,0.00003486198,0.00168072,0.00001239381,0.0001568951,0.01577007],"genre_scores_gemma":[0.936132,0.000001286004,0.06170451,0.00104808,0.0001494096,0.0007188185,0.00004065366,0.00004862729,0.0001566391],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9821254,"threshold_uncertainty_score":0.5694101,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02660127334919866,"score_gpt":0.2982005347852827,"score_spread":0.271599261436084,"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."}}