Higher-codimension points as organizing centers in nonreciprocal pattern-forming systems with O(2) symmetry

Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady and dynamic phases. Complementing the numerical analysis of the field equations with time simulations and path continuation techniques, we derive a reduced dynamical system corresponding to a one-mode approximation for the critical-wavenumber modes. Furthermore, we derive the normal form equations that are valid in the vicinity of the Takens-Bogdanov bifurcation with O(2) symmetry, which allows us to draw on corresponding literature results. Comparing results obtained on the different levels of description, we discuss the bifurcation structure relating trivial uniform and inhomogeneous steady states as well as traveling, standing, and modulated waves. We also contextualize the relevance of recently highlighted features of the linear mode structure, i.e., of the dispersion relations, termed "critical exceptional points" for the transitions between the nonequilibrium phases.