Lari-Lavassani, Ali; Langford, William F.; Huseyin, Koncay; Gatermann, Karin Steady-state mode interactions for \(D_3\) and \(D_4\)-symmetric systems. (English) Zbl 0928.37009 Dyn. Contin. Discrete Impulsive Syst. 6, No. 2, 169-209 (1999). The paper deals with the study of generic bifurcations from a \(D_m\)-invariant equilibrium of a \(D_m\)-symmetric dynamical system \((m=3, 4)\) near points of codimension-2 steady-state mode interactions. The approach is based on techniques of normal forms, blowing-up, unfolding and group theory. The main results of the paper are related to symmetry-breaking bifurcations to primary branches, secondary steady-state and Hopf bifurcations, Bogdanov-Takens symmetry-breaking type bifurcations, as well as the study of the structurally stable heteroclinic cycle in a three dimensional representation of \(D_4\). Reviewer: Vicentiu D.Rădulescu (Craiova) Cited in 2 Documents MSC: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems 37G40 Dynamical aspects of symmetries, equivariant bifurcation theory 37M20 Computational methods for bifurcation problems in dynamical systems 68W30 Symbolic computation and algebraic computation Keywords:symmetric dynamical system; dihedral groups; normal form; symmetric heteroclinic cycle; Hopf bifurcation; blowing-up; unfolding; symmetry-breaking bifurcations; Bogdanov-Takens symmetry PDFBibTeX XMLCite \textit{A. Lari-Lavassani} et al., Dyn. Contin. Discrete Impulsive Syst. 6, No. 2, 169--209 (1999; Zbl 0928.37009)