Abstract

CHAPTER 3. BIFURCATION ANALYSIS 67
Imaginary Part
0.02
0.015
0.01
0.005
0
−0.005
−0.01
−0.015
0.240
0.242
0.244
0.246
0.248
0.250
0.252
0.254
0.256
Bifurcating Eigenvalues on nx=86,nk=72 Grid
−5 −4 −3 −2 −1 0 1 2
x 10 −3
−0.02
Real Part
Figure 3.9: Eigenvalues Creating Oscillatory Solutions
current-voltage plots. Figure 3.10 compares the previous grid results for Nx = 86,
Nk = 72 (about 6,000 unknowns) to the results for the grids Nx = 512, Nk = 2048
(about 1 million unknowns) and Nx = 1024, Nk = 2048 (about 2 million unknowns).
The current-voltage plots of the 1 million unknown and 2 million unknown grids lie
on top of one another. These grids present new physics in the current voltage-plot as
previously shown from the coarser grid. The plot in general is shifted down, having
a smaller global maximum than the coarser grid plot. There are more local minima
and maxima in the refined grid plots as well.