2012/01/02 by Mogens H. Jensen, Jensen, Mogens H., Leo P. Kadanoff +1
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Chaos control and synchronization #Chaotic #Chaotic Dynamics (nlin.CD) #Computer science #Condensed matter physics #Control theory (sociology) #Diagram #Dynamical systems theory #FOS: Physical sciences #Geometry #Irrational number #Mathematics #Nonlinear Dynamics and Pattern Formation #Origins and Evolution of Life #Oscillation (cell signaling) #Phase (matter) #Phase diagram #Physics #Quantum mechanics #Quasiperiodic function #Statistical physics #Synchronization (alternating current) #Topology (electrical circuits) #Variety (cybernetics) #nlin.CD
paper · pdf · doi:10.48550/arxiv.1201.0476
10 pages, 4 figures
arxiv created 2012/01/02 · openalex publication_date 2012/01/02 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another it becomes synchronized, or, as a third possibility, complex chaotic behavior may emerge. With two modes present, like an internal oscillation coupled to a periodic external signal, one obtains a highly structured phase diagram that exhibits these possibilities. In essence, the details are related to the difference between rational and irrational numbers. Natural system can display fragments of this phase diagram, thereby offering insights into their dynamical mechanisms.