{"id":"W2047172093","doi":"10.1115/1.3063629","title":"Simulation of Moment Lyapunov Exponents for Linear Homogeneous Stochastic Systems","year":2009,"lang":"en","type":"article","venue":"Journal of Applied Mechanics","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":30,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Lyapunov exponent; Moment (physics); Mathematics; Stochastic differential equation; Lyapunov function; Applied mathematics; Monte Carlo method; Second moment of area; Lyapunov equation; Statistical physics; Mathematical analysis; Nonlinear system; Physics; Classical mechanics; Statistics; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005348129,0.000376116,0.0005432089,0.0004801349,0.0003586761,0.0004767494,0.0005021034,0.0006002614,0.001029048],"category_scores_gemma":[0.002239708,0.0001550372,0.0003641505,0.0003787098,0.0004171702,0.0004626593,0.0005360995,0.0004588466,0.0001107798],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005274246,"about_ca_system_score_gemma":0.0005202638,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004169611,"about_ca_topic_score_gemma":0.001887463,"domain_scores_codex":[0.9997519,0.00006643745,0.00002122149,0.00003883194,0.00007613199,0.00004552634],"domain_scores_gemma":[0.9988456,0.0007367954,0.0001214189,0.0001002315,0.0001395252,0.00005631192],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00005413926,0.00002698412,0.0007206504,0.00001416241,0.000009372101,0.0000531527,0.00003849236,0.9878417,0.002568281,0.004610075,0.0000933231,0.003969637],"study_design_scores_gemma":[0.000002763189,0.000006601651,0.00004036384,4.17351e-7,8.811121e-7,0.00000222997,0.000001601306,0.999015,0.0005371887,0.0003568173,0.00003481901,0.000001346406],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5065048,0.0001339884,0.4878697,0.0001545395,0.00005141852,0.00009896719,0.0001528614,0.0007531379,0.004280573],"genre_scores_gemma":[0.9621555,0.00004397764,0.03684001,0.00001581792,0.000008052086,0.0000606973,0.00008659179,0.0000185229,0.0007708625],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004169611,"threshold_uncertainty_score":0.008290708,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0168316158690703,"score_gpt":0.23698601173116,"score_spread":0.2201543958620897,"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."}}