A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.
© 1988 The American Physical Society
S. Lichter & A. J. Bernoff, "Stability of Steady Cross-waves: Theory and Experiment," Phys. Rev. A 37 (1988) 1663-1667. DOI:10.1103/PhysRevA.37.1663