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We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
Dynamical system analysis of a universe model which contains matter, radiation, and quintessence with exponential potential, $V \!(\phi)=V_{\!o} \, exp(-\alpha \kappa \phi) \,$, is studied in the light of recent observations and the…
A data-driven approach to elucidating the nature of the dark energy, in the form of a joint analysis of a full set of cosmological parameters, utilizing all available observational data is proposed. A parameterization of a generalized dark…
In this letter we apply dynamical system methods to study all evolutional paths admissible for all initial conditions of the FRW cosmological model with a non-minimally coupled to gravity scalar field and a barotropic fluid. We choose…
The dynamical aspect of accelerating cosmological model has been studied in this paper in the context of modified symmetric teleparallel gravity, the $f(Q)$ gravity. Initially, we have derived the dynamical parameters for two well known…
Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…
This study forges new tools to discriminate between dynamical and static dark energy. It provides accurate evolutionary templates of dynamical cosmological parameters and fundamental constants as analytic functions of the scale factor. They…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
A simple speed-up cosmology model is proposed to account for the dark energy puzzle. We condense contributions from dark energy and curvature term into one effective parameter in order to reduce parameter degeneracies and to find any…
In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution…
Dynamical systems methods are used to investigate cosmological model with non-minimally coupled scalar field. Existence of an asymptotically unstable de Sitter state distinguishes values of the non-minimal coupling constant parameter…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
When intelligent spacecraft or space robots perform tasks in a complex environment, the controllable variables are usually not directly available and have to be inferred from high-dimensional observable variables, such as outputs of neural…
In this article, we examine the dynamical system of the $f(R,\mathcal{G})$ gravity model. This $f(R,G)$ model framework is composed of interactions between dark matter and scalar field through the linear coupling term. The key objective of…
This paper is concerned with string cosmology and the dynamics of multiple scalar fields in potentials that can become negative, and their features as (Early) Dark Energy models. Our point of departure is the "String Axiverse", a scenario…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…