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Theory and applications of Hopf bifurcations in symmetric functional differential equations. (English) Zbl 0917.58027
This paper is devoted to the general theory of Hopf bifurcations in symmetric functional differential equations. This general theory provides some important bifurcation invariants, the so-called crossing numbers, to detect the existence of periodic solutions and to describe their orbits and global continuation. In the paper under review, it is proved that these crossing numbers can be computed from the linearization around equilibria and from the isotypical decomposition of representation spaces. Note that as an application the authors consider the delay-induced oscillations in a Turing ring which provides a model for many biological and chemical systems.
MSC:
37G99Local and nonlocal bifurcation theory