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Discontinuous codimension-two bifurcation in a Vlasov equation
Yoshiyuki Y Yamaguchi1, Julien Barré2
1Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Physical Review. E
|June 17, 2023
Summary
In Vlasov systems, a flat-top stationary state causes discontinuous bifurcations due to weakened resonances. This study details this phenomenon as a codimension-two bifurcation in one-dimensional periodic systems.
Area of Science:
- Plasma physics
- Theoretical physics
- Mathematical physics
Background:
- Vlasov equation describes plasma dynamics.
- Homogeneous stationary states typically exhibit continuous bifurcations.
- Flat-top stationary states are known to weaken resonances.
Purpose of the Study:
- Analyze discontinuous bifurcations in one-dimensional periodic Vlasov systems.
- Investigate the role of resonances in these systems.
- Characterize the underlying bifurcation structure.
Main Methods:
- Analytical techniques applied to Vlasov systems.
- Precise numerical simulations.
- Study of codimension-two bifurcations.
Main Results:
- Demonstrated weakened resonances in flat-top Vlasov systems.
- Identified the bifurcation as discontinuous.
- Related this behavior to a codimension-two bifurcation.
Conclusions:
- The study provides a detailed analysis of discontinuous bifurcations in Vlasov systems.
- Confirms the connection between flat-top states and weakened resonances.
- Offers insights into the complex dynamics of Vlasov systems through bifurcation theory.
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