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Updated: Dec 10, 2025

Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light
Published on: September 20, 2017
Coupled heteroclinic networks in disguise
Maximilian Voit1, Sara Veneziale2, Hildegard Meyer-Ortmanns1
1Department of Physics and Earth Sciences, Jacobs-University Bremen, 28759 Bremen, Germany.
Abstract:
We consider diffusively coupled heteroclinic networks, ranging from two coupled heteroclinic cycles to small numbers of heteroclinic networks, each composed of two connected heteroclinic cycles. In these systems, we analyze patterns of synchronization as a function of the coupling strength. We find synchronized limit cycles, slowing-down states, as well as quasiperiodic motion of rotating tori solutions, transient chaos, and chaos, in general along with multistable behavior. This means that coupled heteroclinic networks easily come in disguise even when they constitute the main building blocks of the dynamics. The generated spatial patterns are rotating waves with on-site limit cycles and perturbed traveling waves from on-site quasiperiodic behavior. The bifurcation diagrams of these simple systems are in general quite intricate.
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