{"id":"W2034333369","doi":"10.1007/s11071-012-0364-8","title":"Estimation of Lyapunov exponents from a time series for n-dimensional state space using nonlinear mapping","year":2012,"lang":"en","type":"article","venue":"Nonlinear Dynamics","topic":"Chaos control and synchronization","field":"Physics and Astronomy","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Lyapunov exponent; Mathematics; Lorenz system; Embedding; Nonlinear system; Series (stratigraphy); Applied mathematics; Lyapunov equation; Mathematical analysis; State space; Attractor; Computer science; Statistics","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":[0.0001228799,0.0001478748,0.0002291724,0.00005573226,0.00009079827,0.0000208386,0.00006830597,0.00004448412,0.00007930036],"category_scores_gemma":[0.00001142344,0.0001491304,0.00008850959,0.0001026346,0.00003074577,0.0003217306,0.00004449404,0.00006792289,0.00001750121],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005983202,"about_ca_system_score_gemma":0.00006513968,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001641324,"about_ca_topic_score_gemma":0.000007847051,"domain_scores_codex":[0.9991466,0.00002396445,0.0002889778,0.000148993,0.0001517676,0.0002397046],"domain_scores_gemma":[0.9993927,0.00007122588,0.0002059526,0.0001515065,0.0001141999,0.00006443039],"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":[0.0007799296,0.002409873,0.1752561,0.000297492,0.001209722,0.000001847566,0.005859927,0.4724831,0.1020193,0.005908124,0.0001814166,0.2335932],"study_design_scores_gemma":[0.0006639034,0.0000183118,0.000852963,0.00004142336,0.00003745763,4.708612e-7,0.00009147757,0.9954155,0.001768605,0.0007937264,0.0001676088,0.000148543],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6579991,0.00002277388,0.340797,0.00004103577,0.0001329359,0.0001856393,0.0007645133,0.00001610313,0.00004084959],"genre_scores_gemma":[0.7491984,6.655741e-7,0.2473715,0.00001220991,0.0004884884,0.000007608428,0.002616704,0.00003222517,0.0002721957],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5229324,"threshold_uncertainty_score":0.6081361,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01081076665315859,"score_gpt":0.2397249517302512,"score_spread":0.2289141850770926,"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."}}