Unraveling Transition and Turbulence Using Nonlinear Optimization

Cherubini, Stefania

doi:10.1007/978-3-030-67902-6_1

Cited by 2 publications

(2 citation statements)

References 45 publications

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“…In reality, very few, if any, physical systems of engineering relevance have globally stable solutions, and unexpected behavior can occur even in well-understood systems, in the case of large perturbations. This issue is demonstrated by numerous examples such as wheel shimmy [1][2][3], machining processes [4,5], robot control [6][7][8], flutter instability [9,10], break squeal [11,12], traffic jams [13,14], electric blackouts [15,16], human balance [17,18], turbulent flows [19][20][21] and prey-predator ecosystems [22,23], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Habib

2023

Preprint

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This paper proposes a novel method for predicting the presence of saddle-node bifurcations in dynamical systems. The method exploits the effect that saddle-node bifurcations have on transient dynamics in the surrounding phase space and parameter space, and does not require any information about the steady-state solutions associated with the bifurcation. Specifically, trajectories of a system obtained for parameters close to the saddle-node bifurcation present local minima of the logarithmic decrement trend in the vicinity of the bifurcation. By tracking the logarithmic decrement for these trajectories, the saddle-node bifurcation can be accurately predicted. The method does not strictly require any mathematical model of the system, but only a few time series, making it directly implementable for gray- and black-box models and experimental apparatus. The proposed algorithm is tested on various systems of different natures, including a single-degree-of-freedom system with nonlinear damping, the mass-on-moving-belt, a time-delayed inverted pendulum, and a pitch-and-plunge wing profile. Benefits, limitations, and future perspectives of the method are also discussed. The proposed method has potential applications in various fields, such as engineering, physics, and biology, where the identification of saddle-node bifurcations is crucial for understanding and controlling complex systems.

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Section: Introductionmentioning

confidence: 99%

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Habib

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In reality, very few, if any, physical systems of engineering relevance have globally stable solutions, and unexpected behavior can occur even in well-understood systems, in the case of large perturbations. This issue is demonstrated by numer-ous examples such as wheel shimmy [1][2][3], machining processes [4,5], robot control [6][7][8], flutter instability [9,10], break squeal [11,12], traffic jams [13,14], pressure relief valves [15], electric blackouts [16,17], human balance [18,19], turbulent flows [20][21][22] and prey-predator ecosystems [23,24], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

Habib

2023

Nonlinear Dyn

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show abstract

Unraveling Transition and Turbulence Using Nonlinear Optimization

Cited by 2 publications

References 45 publications

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

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