Related papers: Bifurcations as dissociation mechanism in bichroma…
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
The ion-electron coupling properties for a ion impurity in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential removing the short-range Coulomb divergence. This work is largely…
In this paper, we investigate periodic vibrations of a group of particles with a dihedral configuration in the plane governed by the Lennard-Jones and Coulomb forces. Using the gradient equivariant degree, we provide a full topological…
It is shown that a molecule can dissociate by the energy transferred from a remote neighbor. This neighbor can be an excited neutral or ionic atom or molecule. If it is an atom, the transferred energy is, of course, electronic and in the…
We study the bifurcation of limit cycles from the periodic orbits of $2n$--dimensional linear centers $\dot{x} = A_0 x$ when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control…
The concept of broken symmetry is used to study bifurcations of equilibria and dynamical instabilities in dynamic model of one-mode laser (nonresonant complex Lorenz model) on the basis of modified Hopf theory. It is shown that an invariant…
The decay of field-free rotational dynamics is experimentally studied in two complementary methods: laser-induced molecular alignment and terahertz-field-induced molecular orientation. Comparison between the decay rates of different…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting $\Gamma \times S^1$-spatial symmetries. The existence of branches…
Nonintegrable dynamical systems have complex structures in their phase space. Motion of a test charged particle in a dipole magnetic field can be reduced to a 2 degree-of-freedom (2 d.o.f.) nonintegrable Hamiltonian system. We carried out a…
Orientation states of two coupled polar molecules controlled by laser pulses are studied theoretically. By varying the period of a series of periodically applied laser pulse, transition from regular to chaotic behavior may occur. Schmidt…
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables…
High harmonic generation in the interaction of femtosecond lasers with atoms and molecules opens the path to molecular orbital tomography and to probe the electronic dynamics with attosecond-{\AA}ngstr\"{o}m resolutions. Molecular orbital…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
We investigate perturbed monomial dynamical system over $\mathbb{F}_p$ given by iterations of $x\mapsto x^n+c\bmod{p}$, where $c\in \mathbb{F}_p$. Instead of study the systems one at a time we study all of them at the same time. The complex…
The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article,…
In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially…
Ultracold molecules can be associated from ultracold atoms by ramping the magnetic field through a Feshbach resonance. A reverse ramp dissociates the molecules. Under suitable conditions, more than one outgoing partial wave can be…
In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, the first order Melnikov…