AI Article Synopsis
- The study investigates how unidirectional coupling between autonomous Duffing oscillators transforms their dynamics from stable equilibrium to more complex behaviors, including periodic and chaotic patterns.
- Both small and large ring configurations of these oscillators are analyzed, emphasizing the influence of unstable periodic solutions on the emergence of chaotic wave patterns and spatiotemporal structures.
- The findings from the theoretical analysis and numerical simulations are validated through a practical experiment using electronic versions of the coupled Duffing oscillators.
Article Abstract
We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators. Particular attention is paid to the role of unstable periodic solutions for the appearance of chaotic rotating waves, spatiotemporal structures, and the Eckhaus effect for a large number of oscillators. Our analytical and numerical results are confirmed by a simple experiment based on the electronic implementation of coupled Duffing oscillators.
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| http://dx.doi.org/10.1063/1.3293176 | DOI Listing |
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