Steady-state mode interactions for D3 and D4-symmetric systems
Steady-state mode interactions for D3 and D4-symmetric systems
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 \(D_4\).
symmetric Bogdanov-Takens bifurcation, symmetric dynamical system, symmetry-breaking bifurcations, Bogdanov-Takens symmetry, symmetry-breaking, blowing-up, Symbolic computation and algebraic computation, symmetric heteroclinic cycle, Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods, blowup, mode interactions, normal form, Dynamical aspects of symmetries, equivariant bifurcation theory, Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems, equivariant bifurcation, Computational methods for bifurcation problems in dynamical systems, dihedral groups, Hopf bifurcation, computer algebra, unfolding
symmetric Bogdanov-Takens bifurcation, symmetric dynamical system, symmetry-breaking bifurcations, Bogdanov-Takens symmetry, symmetry-breaking, blowing-up, Symbolic computation and algebraic computation, symmetric heteroclinic cycle, Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods, blowup, mode interactions, normal form, Dynamical aspects of symmetries, equivariant bifurcation theory, Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems, equivariant bifurcation, Computational methods for bifurcation problems in dynamical systems, dihedral groups, Hopf bifurcation, computer algebra, unfolding
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