... instability sinusoidally varying velocity wave solution fixed point theory bifurcation diagram shock-like wave wave pattern The problem of parametric excitation arises in the study of the dynamic stability of a system [ 1 ]. If the coefficients in the governing differential equations of a system...

... in a parameter plane where attracting fixed points of the phase functions exist. The period-1 instability regions are analytically obtained, and the period-i ( i > 1 ) instability regions are numerically calculated using bifurcation diagrams. The wave patterns corresponding to different instability regions...