STEADY-STATE HOPF MODE INTERACTION AT A SYMMETRY-BREAKING TAKENS-BOGDANOV POINT

This paper is concerned with an example of steady-state/Hopf mode inte raction arising in two-parameter non-linear problems satisfying a Z2-s ymmetry condition. Specifically we study bifurcation phenomena near a symmetry-breaking Takens-Bogdanov point where paths of symmetric stead y-state solutions, symmetric Hopf points and, under a certain positive condition, asymmetric Hopf points intersect. Our approach provides us eful numerical information for switching from one solution path to ano ther. Numerical results are given for an example arising from a finite -element discretization of a problem in fluid mechanics.