Related papers: Reconstructing the parameter space of non-analytic…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
In this work, we have studied the Brans-Dicke (BD) cosmology in anisotropic models. We present three dimensional dynamical system describing the evolution of anisotropic models containing perfect fluid and BD scalar field with…
Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
We investigate the behaviour of the skewness parameters for an anisotropic universe in the framework of General Relativity. Non interacting dark energy is considered in presence of electromagnetic field. A time varying deceleration…
In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
This study explores the dynamics and phase-space behavior of a multi-component dark energy model, where the dark sector consists of a minimally coupled canonical scalar field and the cosmological constant, using a dynamical system analysis…
In this thesis, we used dynamical systems analysis to find the qualitative behaviour of some dark energy models. Specifically, dynamical systems analysis of quintessence scalar field models, chameleon scalar field models and holographic…
We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of…
We investigated a time-varying cosmological constant model using recent BAO measurements from DESI DR2, combined with Type Ia supernova samples (Pantheon$^{+}$, DES-Dovekie, and Union3) and CMB shift parameters, to constrain the…
A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these…
The coincidence problems and other dynamical features of dark energy are studied in cosmological models with variable cosmological parameters and in models with the composite dark energy. It is found that many of the problems usually…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…
Previous work developed a space-time metric with two cosmological scales; one that conveniently describes the classical evolution of the dynamics, and the other describing a scale associated with macroscopic quantum aspects like vacuum…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Models in which dark energy interacts with dark matter have been proposed in the literature to help explain why dark energy should only come to dominate in recent times. In this paper, we present a dynamical framework to calculate…
In this work, we study tracker phantom dark energy models with a general parameterization of the scalar potentials. Our analysis also considers the scenario of having both phantom field and the cosmological constant as the dark energy…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…