2004/06/18 by H. Krivine, Krivine, Hubert, Annick Lesne +3
Physics and Astronomy · #FOS: Physical sciences #Opinion Dynamics and Social Influence #Other Condensed Matter (cond-mat.other) #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.cond-mat/0406432
openalex publication_date 2004/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Discrete autonomous dynamical systems in dimension 1 can exhibit chaotic behavior, whereas the corresponding continuous evolution equations rule it out, and cannot even possess a nontrivial periodic solution. Therefore the passage from discrete to continuous equations (and conversely) is all but harmless. We address this issue and evidence some caveats on the paradigmatic Verhulst logistic equation, investigating in particular the status and influence of the actual size of the unit time step in discrete modelings, rooted in well-known numerical analysis.