On limit cycles arising from the parametric excitation of standing waves

Single-mode limit cycles were recently found as solutions of a nonlinear evolution equation for parametrically excited standing surface waves on liquid in a rectangular container [see Decent and Craik, ''Hysteresis in Faraday resonance'', J. Fluid Mech. 293, 237-268 (1995)]. Here we examine their structure in detail, both analytically and numerically, and describe local and global bifurcations.