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Coupled heteroclinic networks in disguise
Maximilian Voit1, Sara Veneziale2, Hildegard Meyer-Ortmanns1
1Department of Physics and Earth Sciences, Jacobs-University Bremen, 28759 Bremen, Germany.
Coupled heteroclinic networks exhibit complex synchronization patterns, including synchronized cycles, chaos, and multistability. These dynamics reveal intricate spatial patterns like rotating waves and perturbed traveling waves.
Area of Science:
- Dynamical Systems and Network Science
- Nonlinear Dynamics and Chaos Theory
Background:
- Heteroclinic networks are fundamental structures in nonlinear dynamics.
- Understanding synchronization in coupled complex systems is crucial for various scientific fields.
Purpose of the Study:
- To investigate synchronization phenomena in diffusively coupled heteroclinic networks.
- To analyze the emergence of complex dynamics and spatial patterns as a function of coupling strength.
Main Methods:
- Analysis of coupled heteroclinic networks, from two cycles to small networks.
- Systematic examination of synchronization patterns across varying coupling strengths.
Main Results:
- Observed synchronized limit cycles, slowing-down states, quasiperiodic motion, transient chaos, and chaos.
- Identified multistable behavior and intricate bifurcation diagrams.
- Generated spatial patterns including rotating waves and perturbed traveling waves.
Conclusions:
- Coupled heteroclinic networks display rich and often disguised dynamical behaviors.
- Synchronization strength significantly influences the emergent patterns and complexity.
- These systems serve as foundational models for complex network dynamics.
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