We propose a method for studying symmetric global Hopf bifurcation problems in a parabolic system. The objective is to detect unbounded branches of non-constant periodic solutions that arise from an equilibrium point and describe their symmetric properties in detail. The method is based on the twisted equivariant degree theory, which counts orbits of solutions to symmetric equations, similar to the usual Brouwer degree, but on the report of their symmetric properties.
Equivariant Global Hopf Bifurcation in Abstract Nonlinear Parabolic Equations
Arnaja Mitra, The University of Texas at DallasAuthors: Zalman Balanov, Wieslaw Krawcewicz, Arnaja Mitra, Dmitrii Rachinskii
2023 AWM Research Symposium