Related papers: Cosmological global dynamical systems analysis
There have been thousands of cosmological models for our early universe proposed in the literature, and many of them claimed to be able to give rise to scale-invariant power spectrum as was favored by the observational data. It is thus…
In this paper, we derive the field equations of modified Gauss-Bonnet gravity termed as $f(R,G)$ gravity for the non-flat Friedmann-Robertson-Walker (FRW) spacetime. We utilize the dynamical system approach to study the cosmic dynamics of…
We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium…
We perform a detailed analysis for the dynamics of Chiral cosmology in a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe with a mixed potential term. The stationary points are categorized in four families. Previous results…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…
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…
In this work, we have carried on dynamical system analysis of hessence field coupling with dark matter in $f(T)$ gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is non-linear. So, we…
Classically, the dynamics in a non-globally hyperbolic spacetime is ill posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second order operator acting on a Hilbert space defined on static…
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…
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional…
We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…
We establish a general thermodynamic scheme for cosmic fluids with internal self-interactions and discuss equilibrium and non-equilibrium aspects of such systems in connection with (generalized) symmetry properties of the cosmological…
We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by…
We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre…
Horndeski models with a de Sitter critical point for any kind of material content may provide a mechanism to alleviate the cosmological constant problem. We study the cosmological evolution of two classes of families - the linear models and…
Solutions to flat space Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant are investigated. The matter is modelled as a $\gamma$-law perfect fluid. The field equations are reduced from fourth order to…
The stable critical points and their corresponding cosmology are derived in the teleparallel gravity with an added Gauss-Bonnet topological invariant term. We have analyzed the dynamics of the Universe by presenting two cosmological viable…
Some cosmological models based on the gravitational theory $f(R) = R+\zeta R^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different…