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The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
In this talk we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a collapsing universe (for a given…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
The study addresses matter-coupled modified gravity, particularly $f (T, \mathcal{T})$ gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of…
The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis,…
We apply dynamical systems techniques to investigate cosmological models inspired in scalar-tensor theories written in the Einstein frame. We prove that if the potential and the coupling function are sufficiently smooth functions, the…
We study cosmological evolutions of the generalized model of nonlinear massive gravity in which the graviton mass is given by a rolling scalar field and is varying along time. By performing dynamical analysis, we derive the critical points…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and…
We investigate an interacting quintessence dark energy - dark matter scenario and its impact on structure formation by analyzing the evolution of scalar perturbations. The interaction is introduced by incorporating a non-zero source term…
In this paper we exploit the theory of the dynamical systems to study the dynamics of the standard cosmological model of the universe, which is known as the $\Lambda$CDM model. We assume that the matter content in our universe consists of…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
A new mechanism of adjustment of vacuum energy down to the observed value from an initially huge one is considered. The mechanism is based on a very strong variation of the gravitational coupling constant in very early universe. The model…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We construct a viable cosmological model based on velocity diffusion of matter particles. In order to ensure the conservation of the total energy-momentum tensor in the presence of diffusion, we include a cosmological scalar field $\phi$…
We investigate a dynamical reconstruction of the dark energy equation of state parameter by assuming that it satisfies a law of motion described by an autonomous second-order differential equation, with the limit of the cosmological…
The present thesis is devoted to the non-parametric reconstruction of some cosmological parameters using diverse observational datasets. The Universe is assumed to be spatially homogeneous and isotropic, thus described by the FLRW metric.…
We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and…
The cosmological model with an interaction between dynamical quintessence dark energy and cold dark matter is considered. Evolution of a dark energy equation of state parameter is defined by a dark energy adiabatic sound speed and a dark…
This thesis employs the dynamical systems approach to explore two cosmological models: an anisotropic dark energy scenario in a Bianchi-I background and the Generalized SU(2) Proca (GSU2P) theory in a flat FLRW background. In the first…