Universality of discontinuous bifurcations in collisionless dynamics

Area of Science:

• Nonlinear Dynamics
• Plasma Physics
• Fluid Dynamics

Background:

• Bifurcations are critical points in dynamical systems where qualitative behavior changes.
• Codimension-two bifurcations involve multiple parameters and exhibit complex dynamics.
• Understanding these bifurcations is crucial for modeling phenomena in various scientific fields.

Purpose of the Study:

• To investigate the universality of collisionless nonlinear dynamics at a codimension-two bifurcation.
• To analyze the scenario where two eigenvalues collide at the origin, leading to continuous and discontinuous bifurcations.
• To demonstrate the occurrence of this specific bifurcation in relevant physical systems.

Main Methods:

• Linear analysis of eigenvalue behavior near the origin.
• Direct numerical simulations of the dynamical system.
• Application of methods to both two-dimensional shear flows and repulsive plasma-mimicking systems.

Main Results:

• The codimension-two bifurcation was confirmed to occur.
• Evidence of both continuous bifurcation lines and discontinuous jump lines meeting at the bifurcation point was found.
• The bifurcation was observed in both shear flow models and plasma simulations.

Conclusions:

• The investigated codimension-two bifurcation is a robust phenomenon in collisionless nonlinear dynamics.
• This bifurcation mechanism is relevant for diverse systems, including fluid dynamics and plasma physics.
• The findings contribute to a deeper understanding of complex system behavior and transitions.