{"id":"W4416785449","doi":"10.28924/2291-8639-23-2025-303","title":"Codimension-One Bifurcation Analysis and Chaos of a Discrete Competition Duopoly Game","year":2025,"lang":"","type":"article","venue":"International Journal of Analysis and Applications","topic":"Merger and Competition Analysis","field":"Economics, Econometrics and Finance","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Duopoly; Chaotic; Quasiperiodic function; Invariant (physics); Bifurcation; Nonlinear system; Competition (biology); Cournot competition","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008551161,0.0002336955,0.001288502,0.005573161,0.0001506963,0.0002120669,0.0004187011,0.0001306994,0.0009149299],"category_scores_gemma":[0.00007162309,0.0002630193,0.001020957,0.004419636,0.000294314,0.0002896563,0.0001339747,0.0002229348,0.000009978327],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001021827,"about_ca_system_score_gemma":0.00006727246,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003717221,"about_ca_topic_score_gemma":0.0001980602,"domain_scores_codex":[0.9967056,0.00007498647,0.002315236,0.000468461,0.0002651161,0.0001706087],"domain_scores_gemma":[0.9956645,0.0001783528,0.002529034,0.0003774103,0.001089634,0.0001610675],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"observational","study_design_scores_codex":[0.0001388173,0.0009438795,0.2703141,0.00008780139,0.07149194,0.00000281339,0.0004815435,0.003906668,0.0009764513,0.6401706,0.00007370192,0.01141172],"study_design_scores_gemma":[0.002428806,0.0001951021,0.7612127,0.0002470244,0.04062171,0.00001487954,0.00115433,0.1045139,0.001470755,0.06796521,0.01939258,0.0007830146],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1176649,0.007482606,0.8650956,0.00626799,0.0001876432,0.0002104743,0.0005849416,0.000007503731,0.002498419],"genre_scores_gemma":[0.9832596,0.01412576,0.001348699,0.0002419478,0.0001445602,0.00002180357,0.0001807229,0.000009012856,0.0006679074],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8655947,"threshold_uncertainty_score":0.9999984,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01053325199315683,"score_gpt":0.2569349874507296,"score_spread":0.2464017354575728,"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."}}