Hamiltonian Hopf bifurcation with symmetry
نویسندگان
چکیده
In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not generically exist in the dissipative framework. The theoretical study is illustrated with several examples.
منابع مشابه
Branches of Stable Three{tori Using Hamiltonian Methods in Hopf Bifurcation on a Rhombic Lattice
This paper uses Hamiltonian methods to nd and determine the stability of some new solution branches for an equivariant Hopf bifurcation on C 4. The normal form has a symmetry group given by the semi-direct product of D2 with T 2 S 1. The Hamiltonian part of the normal form is completely integrable and may be analyzed using a system of invariants. The idea of the paper is to perturb relative equ...
متن کاملA Hamiltonian Analogue of the Meandering Transition
In this paper a Hamiltonian analogue of the well-known meandering transition from rotating waves to modulated rotating and modulated travelling waves in systems with the Euclidean symmetry of the plane is presented. In non-Hamiltonian systems, for example in spiral wave dynamics, this transition is a Hopf bifurcation in a corotating frame, as external parameters are varied, and modulated travel...
متن کاملThe Constrained Liapunov - Schmidt Procedure and Periodic Orbits
This paper develops the Liapunov-Schmidt procedure for systems with additional constraints such as having a first integral, being Hamiltonian, or being a gradient system. Similar developments for systems with symmetry, including reversibility, are well known, and the method of this paper augments and is consistent with that approach. One of the results states that the bifurcation equation for H...
متن کاملBifurcations of the Hamiltonian Fourfold 1: 1 Resonance with Toroidal Symmetry
This paper deals with the analysis of Hamiltonian Hopf as well as saddle-centre bifurcations in 4-DOF systems defined by perturbed isotropic oscillators (1:1:1:1 resonance), in the presence of two quadratic symmetries Ξ and L1. When we normalize the system with respect to the quadratic part of the energy and carry out a reduction with respect to a 3-torus group we end up with a 1-DOF system wit...
متن کاملHOPF BIFURCATION CONTROL WITH PD CONTROLLER
In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
متن کامل