Global and Local: Synchronization and Emergence

Details Global and Local: Synchronization and Emergence Global and Local: Synchronization and Emergence

2012-01-02

arxiv.org/abs/1201.0476v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 4 figures

Scientific paper

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.

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