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Many physical systems, including classical fluids, present in their phase diagram the competition between two phases that are separated by a line of first-order phase transitions which terminates at a so-called critical point. Despite…
The flows of phase trajectories of cosmological models based on the vacuum classical Higgs field and their behavior on the Einstein-Higgs surface near singular points of a dynamical system are investigated by numerical simulation. The…
We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting…
A detailed qualitative analysis and numerical modeling of the evolution of cosmological models based on nonlinear classical and phantom scalar fields with self-action are performed. Complete phase portraits of the corresponding dynamical…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…
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…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
Our work deals with the dynamical system analysis of quintessence dark energy scalar field model with exponential potential. A dynamical system analysis has been applied at the background level. Using suitable transformation of variables,…
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…
One possible description for the current accelerated expansion of the universe is quintessence dynamics. The basic idea of quintessence consists of analyzing cosmological scenarios driven by scalar fields. In this work we present some…
A detailed comparative qualitative analysis and numerical simulation of evolution of the cosmological models based on classical and phantom scalar fields with self-action was performed. The phase portraits of the dynamic systems of…
We extend the investigation of cosmological dynamics of the general non-canonical scalar field models by dynamical system techniques for a broad class of potentials and coupling functions. In other words, we do not restrict the analysis to…
We investigate dynamics of scalar field with non-minimal kinetic term. Nontrivial behavior of the field in the vicinity of singular points of kinetic term is observed. In particular, the singular points could serve as attractor for…
Generalised axion-like scalar fields provide a well-motivated framework for describing the late-time acceleration of the Universe. As the field evolves, it rolls down its potential and, depending on its mass and initial conditions, it may…
The work deals with homogeneous and isotropic, flat FRW model of the universe which is filled up with non-interacting dark matter and dark energy to compatible with recent observational evidences. By choosing the dark energy in the form of…
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…
We study the dynamics of a non-minimally coupled scalar field cosmology with a potential function. We use the framework of dynamical systems theory to investigate all evolutional paths admissible for all initial conditions. Additionally, we…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
We derive generic equations for a vector field driving the evolution of flat homogeneous isotropic universe and give a comparison with a scalar filed dynamics in the cosmology. Two exact solutions are shown as examples, which can serve to…