Related papers: Tracking quintessence: a dynamical systems study
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
Perpetual points (PPs) are special critical points for which the magnitude of acceleration describing dynamics drops to zero, while the motion is still possible (stationary points are excluded), e.g. considering the motion of the particle…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
Quintessence theories for cosmic acceleration imbue dark energy with a non-trivial dynamics that offers hope in distinguishing the physical origin of the component. We review quintessence models with an emphasis on this dynamics and discuss…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
Criteria are presented for testing whether every trajectory of a dynamic integer system converges to the same fixed point
A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy,…
The accurate visual tracking of a moving object is a human fundamental skill that allows to reduce the relative slip and instability of the object's image on the retina, thus granting a stable, high-quality vision. In order to optimize…
The properties of quintessence are examined through the study of the variation of the electromagnetic coupling. We consider two simple quintessence models with a modified exponential potential and study the parameter space constraints…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
The main objective of tracking control is to steer the tracking error, that is the difference between the reference and the output, to zero while the plant's operation limits are satisfied. This requires that some assumptions on the…
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…
Recent observations indicate that the universe's expansion has been accelerating of late. But recent theoretical work has highlighted the difficulty of squaring acceleration with the underlying assumptions of string theory, disfavoring most…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Within present constraints on the observed smooth energy and its equation of state parameter, it is important to find out whether the smooth energy is static (cosmological constant) or dynamic (quintessence). The most dynamical quintessence…
In a multi-modeling based approach, the system under development is described by several models that represent various perspectives and concerns. Obviously, these partial representations are less complex than the global model, but they need…