On limit cycles arising from the parametric excitation of standing waves

Decent, S.P. and Craik, A.D.D. (1997) On limit cycles arising from the parametric excitation of standing waves. Wave Motion, 25 (3). pp. 275-294. ISSN 0165-2125

Abstract

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.