Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Nonlinear Dynamics, Synchronization and Chaos

DY 31.2: Talk

Wednesday, April 3, 2019, 10:15–10:30, H20

Separation of scales in a hierarchical heteroclinic network — •Maximilian Voit and Hildegard Meyer-Ortmanns — Jacobs University Bremen, Bremen, Germany

In the context of winnerless competition we consider a heteroclinic network with a structural hierarchy.[1] It contains two levels of cyclic competition. The lower level is realized by simple heteroclinic cycles between saddle equilibria. The higher level, on the other hand, consists of a heteroclinic cycle whose saddles are the lower level heteroclinic cycles. As a consequence, two different time scales emerge in this system. By a Poincaré map method we derive an analytic description of this dynamics. We thereby show how to predict the ratio between time scales depending on parameters and initial conditions.

[1] M. Voit and H. Meyer-Ortmanns (2018) to be pub. in EPJ ST