Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry.
Bifurcations for Turing instability without SO(2) symmetry
In this paper, we consider the Swift–Hohenberg equation with perturbed boundary conditions. We do not a priori know the eigenfunctions for the linearized problem since the symmetry of the problem is broken by perturbation. We show that how the neutral stability curves change and, as a result, how the bifurcation diagrams change by the perturbation of the boundary conditions.
Codimension 4 singularities on reflectionally symmetryc planar vector fields.
The paper deals with the topological classification of singularities of vector fields on the plane which are invariant under reflection with respect to a line. As it has been proved in previous papers, such a classification is necessary to determine the different topological types of singularities of vector fiels on R3 whose linear part is invariant under rotations. To get the classification we use normal form theory and the the blowing-up method.
Equivariant Hopf bifurcation in a ring of identical cells with delay.
Generic bifurcation of reversible vector fields on a 2-bidimensional manifold.
In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
Hopf bifurcation with -symmetry.
Integral equations and exponential trichotomy of skew-product flows.
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system.
On lopsided systems.
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
Path formulation for multiparameter -equivariant bifurcation problems
We implement a singularity theory approach, the path formulation, to classify -equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a -miniversal unfolding of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of onto its unfolding parameter space. We apply our results to degenerate...
Periodic solutions of second order hamiltonian systems bifurcating from infinity
Speciation: A case study in symmetric bifurcation theory.
The Art and Science of Symmetric Design