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  4. Early Effect in Time-Dependent, High-Dimensional Nonlinear Dynamical Systems With Multiple Resonances
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Early Effect in Time-Dependent, High-Dimensional Nonlinear Dynamical Systems With Multiple Resonances

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Title
Early Effect in Time-Dependent, High-Dimensional Nonlinear Dynamical Systems With Multiple Resonances
Description

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

Date Created
2015-02-09
Contributors
  • Park, Youngyong (Author)
  • Do, Younghae (Author)
  • Altmeyer, Sebastian (Author)
  • Lai, Ying-Cheng (Author)
  • Lee, GyuWon (Author)
  • Ira A. Fulton Schools of Engineering (Contributor)
Resource Type
Text
Extent
7 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
ASU Scholarship Showcase
Peer-reviewed
No
Open Access
No
Series
PHYSICAL REVIEW E
Handle
https://hdl.handle.net/2286/R.I.29574
Preferred Citation

Park, Youngyong, Do, Younghae, Altmeyer, Sebastian, Lai, Ying-Cheng, & Lee, GyuWon (2015). Early effect in time-dependent, high-dimensional nonlinear dynamical systems with multiple resonances. PHYSICAL REVIEW E, 91(2), 0-0. http://dx.doi.org/10.1103/PhysRevE.91.022906

Level of coding
minimal
Cataloging Standards
asu1
System Created
  • 2015-05-27 03:28:56
System Modified
  • 2021-10-29 11:45:10
  •     
  • 2 years 1 month ago
Additional Formats
  • OAI Dublin Core
  • MODS XML

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