Coupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov-Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in C2of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.
|Original language||English (US)|
|Number of pages||26|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - 1987|
ASJC Scopus subject areas