Related papers: PI-controlled bioreactor as a generalized Lienard …
Effect of external periodic force on an oscillatory order in a reaction diffusion system (Gierer Meinhardt model) has been investigated. The 2:1 resonance situation is found susceptible for the generation of a band of phase instabilities.…
This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
We study measurement-induced phase transitions in quantum circuits consisting of kicked Ising models with postselected weak measurements, whose dynamics can be mapped onto a classical dynamical system. For a periodic (Floquet) non-unitary…
Resonant driving of electronic transitions with coherent laser sources creates quantum coherent superpositions of the involved electronic states. Most time-resolved studies have focused on gases or isolated subsystems embedded in insulating…
We investigate the emergent open dynamics of a quantum system that undergoes rapid repeated unitary interactions with a sequence of ancillary systems. We study in detail how decoherence appears as a subleading effect when a quantum system…
We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and…
In this paper we discuss how a general bilinear finite-dimensional closed quantum system with dispersed parameters can be steered between eigenstates. We show that, under suitable conditions on the separation of spectral gaps and the…
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary…
The general context of this work is the feedback control of an infinite-dimensional system so that the closed-loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically,…
Spectral properties of fluorescent radiation from a two-level quantum system with broken inversion spatial symmetry, which can be described by a model of an one-electron two-level atom whose electric dipole moment operator has permanent…
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…
We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic…
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
A mechanism for orientation of bilayer classical Wigner crystals in a piezoelectric medium is considered. For the GaAs system the piezoelectric correction to the electrostatic interaction between electrons is calculated. It is shown that…
We study the generation of electronic ring currents in the presence of nonadiabatic coupling using circularly polarized light. For this, we introduce a solvable model consisting of an electron and a nucleus rotating around a common center…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
We present a control-theoretic analysis of the system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that by applying external fields with just two resonant frequencies, any desired unitary operator can…
We present a differential rate equation model of chiral polymerization based on a simple copolymerization scheme in which the enantiomers are added to, or removed from, the homochiral or heterochiral chains (reversible stepwise isodesmic…