Hopf bifurcation and the beam-plasma instability [unknown]

John David Crawford
1984 Contemporary Mathematics   unpublished
For finite mode instabilities in dissipative systems, invariant manifold methods allow the bifurcation analysis to be reduced to the locally attracting center manifold. In a kinetic model of electron plasma dynamics, these methods are applied to the one mode beam-plasma instability which occurs via Hopf bifurcation. The instability results in a nonlinear oscillation, and the amplitude equation can be solved to describe the time asymptotic state.
doi:10.1090/conm/028/751996 fatcat:r2nsx354pzeb5pjjb6w75d55gq