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Symmetry-breaking in coupled, identical, fast–slow systems produces a rich, dramatic variety of dynamical behavior—such as amplitudes and frequencies differing by an order of magnitude or more and qualitatively different rhythms between oscillators, corresponding to different functional states. We present a novel method for analyzing these systems. It identifies the key geometric structures responsible for this new symmetry-breaking, and it shows that many different types of symmetry-breaking rhythms arise robustly. We find symmetry-breaking rhythms in which one oscillator exhibits small-amplitude oscillations, while the other exhibits phase-shifted small-amplitude oscillations, large-amplitude oscillations, mixed-mode oscillations, or even undergoes an explosion of limit cycle canards. Two prototypical fast–slow systems illustrate the method: the van der Pol equation that describes electrical circuits and the Lengyel–Epstein model of chemical oscillators.
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Transition to Limit-Cycle Oscillation in Fluid-Structure Interactions: Mutual Correlations and Causal Dependencies
We investigate the dynamic characteristics corresponding to the structural fluctuations of a cantilever suspended in a turbulent flow. To investigate the intricate dynamics of the flow–structure interaction, first, we explore the ability of network analysis to identify the different dynamic states and probe the viability of using quantifiers of network topology as precursors for the onset of limit-cycle oscillations. By increasing the Reynolds number, we observe that the structural oscillations, measured using a strain gauge, transition from low-amplitude chaotic oscillations to large-amplitude periodic oscillations associated with limit-cycle oscillations. We characterize the dynamic states of the system by constructing the weighted correlation network from the time series of strain and identifying the network properties that have the potential to be used as precursors for the onset of limit-cycle oscillations. Furthermore, we use Pearson correlation to illustrate the evolution of mutual statistical influence between the structural oscillations and the flowfield. We use this information and the Granger causality to identify the causal dependence between the structural oscillations and velocity fluctuations. By identifying the causal variable during each regime, we illustrate the directional dependence through a cause–effect relationship in this flow–structure interaction as it transitions to limit-cycle oscillations.
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- Award ID(s):
- 2053671
- PAR ID:
- 10406144
- Date Published:
- Journal Name:
- AIAA Journal
- Volume:
- 61
- Issue:
- 4
- ISSN:
- 0001-1452
- Page Range / eLocation ID:
- 1475 to 1484
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.2514/1.J062082
