Related papers: Tracking quintessence: a dynamical systems study
In this paper we consider the problem of stabilization and tracking of desired state trajectory for a wide range of nonlinear control problems with disturbances. We present the sufficient conditions for the existence of $C^k$ state feedback…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
Tracking single fluorescent molecules has offered resolution into dynamic molecular processes at the single-molecule level. This perspective traces the evolution of single-molecule tracking, highlighting key developments across various…
In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
We perform for the first time a dynamical system analysis of both the background and perturbation equations, of $\Lambda$CDM cosmology and quintessence scenario with an exponential potential. In the former case the perturbations do not…
A short review of some of the aspects of quintessence model building is presented. We emphasize the role of tracking models and their possible supersymmetric origin.
Object tracking systems play important roles in tracking moving objects and overcoming problems such as safety, security and other location-related applications. Problems arise from the difficulties in creating a well-defined and…
We use a dynamical systems approach to study thawing quintessence models, using a multi-parameter extension of the exponential potential which can approximate the form of typical thawing potentials. We impose observational constraints using…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical…
We study the dynamics of a quintessence model based on two interacting scalar fields. The model can account for the (recent) accelerated expansion of the Universe suggested by astronomical observations. Acceleration can be permanent or…
Single-object tracking is a well-known and challenging research topic in computer vision. Over the last two decades, numerous researchers have proposed various algorithms to solve this problem and achieved promising results. Recently,…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Tracking transforming objects holds significant importance in various fields due to the dynamic nature of many real-world scenarios. By enabling systems accurately represent transforming objects over time, tracking transforming objects…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…