Related papers: Unfolding a Codimension-Two, Discontinuous, Andron…
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of…
Many physical systems exhibit limit cycle oscillations induced by Hopf bifurcations. In aerospace engineering, limit cycle oscillations arise from undesirable Hopf bifurcation phenomena such as aeroelastic flutter and transonic buffet. In…
A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer for a parameters range where the Hopf bifurcation occurs in the…
We investigate the universality in collisionless nonlinear dynamics of a codimension-two bifurcation where two eigenvalues collide at the origin, and two lines of continuous bifurcation and discontinuous jump meet. Through linear analysis…
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a…
We study the semiclassical limit of the anisotropic two-photon Dicke model with a dissipative bosonic field and describe its rich nonlinear dynamics. Besides normal and 'superradiant'-like phases, the presence of localized fixed points…
A delayed differential equation modelling a single neuron with inertial term is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a…
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…
The slow passage through a Hopf bifurcation leads to the delayed appearance of large amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium…
This paper presents results concerning bifurcations of 2D piecewise-smooth vector fields. In particular, the generic unfoldings of codimension three fold-addle singularities of Filippov systems, where a boundary-saddle and a fold coincide,…
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…
We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also…
We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones and D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotech., 71:105-131,…
In this paper, the equivariant degree theory is used to analyze the occurrence of the Hopf bifurcation under effectively verifiable mild conditions. We combine the abstract result with standard interval polynomial techniques based on…
We investigate the stability loss of invariant n-dimensional quasi-periodic tori during a double Hopf bifurcation, where at bifurcation the two normal frequencies are in normal-normal resonance. Invariants are used to analyse the normal…
We study a two-fluid description of high and low temperature components of the electron velocity distribution of an idealized tokamak plasma. We refine previous results on the laminar steady-state solution. On the one hand, we prove global…
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with…
In this paper are studied the codimensions one, two, three and four Hopf bifurcations and the pertinent Lyapunov stability coefficients. Algebraic expressions obtained with computer assisted calculations are displayed.
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization…