scholarly journals Dynamical system analysis of self-interacting three-form field cosmological model: stability and bifurcation

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Soumya Chakraborty ◽  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dynamical System ◽  
Cosmological Model ◽  
Critical Points ◽  
Cold Dark Matter ◽  
System Analysis ◽  
Evolution Equations ◽  
Equilibrium Points ◽  
Index Theory ◽  
Model Stability ◽  
Form Field

AbstractThe present work deals with Cosmological model of a three-form field, minimally coupled to gravity and interacting with cold dark matter in the background of flat FLRW space-time. By suitable choice of the dimensionless variables, the evolution equations are converted to an autonomous system and cosmological study is done by dynamical system analysis. The critical points are determined and the stability of the (non-hyperbolic) equilibrium points are examined by center manifold Theory. Possible bifurcation scenarios have been examined by the Poincaré index theory to identify possible cosmological phase transition. Also stabilities of the critical points have been analyzed globally using geometric features.

scholarly journals Dynamical system analysis of three-form field dark energy model with baryonic matter

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Soumya Chakraborty ◽  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
Cold Dark Matter ◽  
System Analysis ◽  
Evolution Equations ◽  
Matter Field ◽  
Baryonic Matter ◽  
Form Field ◽  
The Stability ◽  
Manifold Theory

AbstractA cosmological model having matter field as (non) interacting dark energy (DE) and baryonic matter and minimally coupled to gravity is considered in the present work with flat FLRW space time. The DE is chosen in the form of a three-form field while radiation and dust (i.e; cold dark matter) are the baryonic part. The cosmic evolution is studied through dynamical system analysis of the autonomous system so formed from the evolution equations by suitable choice of the dimensionless variables. The stability of the non-hyperbolic critical points are examined by Center manifold theory and possible bifurcation scenarios have been examined.

scholarly journals Dynamical system analysis of a five-dimensional cosmological model

2018 ◽  
Vol 363 (10) ◽  
Author(s):  
A. Savaş Arapoğlu ◽  
Ezgi Yalçınkaya ◽  
A. Emrah Yükselci
Keyword(s):  
Dynamical System ◽  
Cosmological Model ◽  
System Analysis

scholarly journals Cosmological dynamics of f(R) models in dynamical system analysis

2020 ◽  
Vol 35 (22) ◽  
pp. 2050124
Author(s):  
Parth Shah ◽  
Gauranga C. Samanta
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Critical Points ◽  
System Analysis ◽  
Late Time ◽  
Field Equations ◽  
Acceleration Phase ◽  
First Case ◽  
Acceleration Of The Universe ◽  
The Universe

In this work we try to understand the late-time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models [Formula: see text] and [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] for the study. As a first case we fix the value of [Formula: see text] and analyze for all [Formula: see text]. Later as second case, we fix the value of [Formula: see text] and calculation are done for all [Formula: see text]. At the end all the calculations for the generalized case have been shown and results have been discussed in detail.

A non-canonical scalar field cosmological model: Stability and bifurcation analysis

2019 ◽  
Vol 34 (32) ◽  
pp. 1950261
Author(s):  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Phase Transition ◽  
Scalar Field ◽  
Critical Points ◽  
Autonomous System ◽  
System Analysis ◽  
Field Equations ◽  
Model Stability ◽  
Change Of Variables ◽  
Manifold Theory ◽  
Canonical Scalar Field

In this work, cosmological implications of a non-canonical scalar field model have been studied in the background of homogeneous and isotropic flat FLRW spacetime by using dynamical system analysis. By suitable change of variables, the field equations are transformed to an autonomous system and the stability of the system of critical points are examined. For hyperbolic critical points, the analysis of the system is done by using Hartman–Grobman theorem, while the center manifold theory is used to study non-hyperbolic critical points. It is found that the parameters in the autonomous system play a crucial role for phase transition of the Universe. Finally, possible bifurcation scenarios are discussed to identify the point of phase transition.

scholarly journals Interacting dark energy model in the brane scenario: A dynamical system analysis

2019 ◽  
Vol 16 (08) ◽  
pp. 1950115
Author(s):  
Sujay Kr. Biswas ◽  
Subenoy Chakraborty
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Scalar Field ◽  
Critical Points ◽  
System Analysis ◽  
Evolution Equations ◽  
Field Potential ◽  
Brane Cosmology ◽  
Brane Model ◽  
Barotropic Equation

The present work is a second in the series of investigations of the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here, dark matter is chosen in the form of perfect fluid with barotropic equation of state, while a real scalar field with self-interacting potential is chosen as dark energy. The scalar field potential is chosen as exponential or hyperbolic in nature and three different choices for the interactions between the dark species are considered. In the background of spatially flat, homogeneous and isotropic Friedmann–Robertson–Walker (FRW) brane model, the evolution equations are reduced to an autonomous system by suitable transformation of variables and a series of critical points are obtained for different interactions. By analyzing the critical points, we have found a cosmologically viable model describing an early inflationary scenario to dark energy-dominated era connecting through a matter-dominated phase.

Dynamical system analysis of the Bianchi type-V cosmological model in R n -gravity

2021 ◽  
Vol 38 (20) ◽  
pp. 205004
Author(s):  
Thato Tsabone ◽  
Amare Abebe
Keyword(s):  
Dynamical System ◽  
Cosmological Model ◽  
System Analysis ◽  
Bianchi Type ◽  
Type V ◽  
Bianchi Type V

scholarly journals Kosambi–Cartan–Chern (KCC) theory for higher-order dynamical systems

2016 ◽  
Vol 13 (02) ◽  
pp. 1650014 ◽  
Author(s):  
Tiberiu Harko ◽  
Praiboon Pantaragphong ◽  
Sorin V. Sabau
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Cold Dark Matter ◽  
Evolution Equations ◽  
Dynamical Evolution ◽  
Finsler Spaces ◽  
Stability And Instability ◽  
The Relationship ◽  
Autonomous Dynamical Systems

The Kosambi–Cartan–Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, with the solution curves of the dynamical system described by methods inspired by the theory of geodesics in a Finsler spaces. The evolution of a dynamical system is geometrized by introducing a nonlinear connection, which allows the construction of the KCC covariant derivative, and of the deviation curvature tensor. In the KCC theory, the properties of any dynamical system are described in terms of five geometrical invariants, with the second one giving the Jacobi stability of the system. Usually, the KCC theory is formulated by reducing the dynamical evolution equations to a set of second-order differential equations. In this paper, we introduce and develop the KCC approach for dynamical systems described by systems of arbitrary [Formula: see text]-dimensional first-order differential equations. We investigate in detail the properties of the [Formula: see text]-dimensional autonomous dynamical systems, as well as the relationship between the linear stability and the Jacobi stability. As a main result we find that only even-dimensional dynamical systems can exhibit both Jacobi stability and instability behaviors, while odd-dimensional dynamical systems are always Jacobi unstable, no matter their Lyapunov stability. As applications of the developed formalism we consider the geometrization and the study of the Jacobi stability of the complex dynamical networks, and of the [Formula: see text]-Cold Dark Matter ([Formula: see text]CDM) cosmological models, respectively.

scholarly journals Dynamical system analysis of three fluid cosmological model

2020 ◽  
Author(s):  
Nilanjana Mahata ◽  
Subenoy Chakraborty
Keyword(s):  
Dynamical System ◽  
Cosmological Model ◽  
System Analysis

Dynamical system analysis for a scalar–tensor model with Gauss–Bonnet coupling

2019 ◽  
Vol 16 (03) ◽  
pp. 1950044
Author(s):  
Behnaz Fazlpour ◽  
Ali Banijamali
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
Scalar Field ◽  
Critical Points ◽  
System Analysis ◽  
Field Potential ◽  
Tensor Model ◽  
Coincidence Problem ◽  
Perturbation Matrix ◽  
Dynamical System Method

In this paper, we study the dynamics of a scalar–tensor model of dark energy in which a scalar field that plays the role of dark energy, non-minimally coupled to the Gauss–Bonnet invariant in four dimensions. We utilize the dynamical system method to extract the critical points of the model and to conclude about their stability, we investigate the sign of the corresponding eigenvalues of the perturbation matrix at each point numerically. For exponential form of the scalar field potential and coupling function, we find five stable points among the critical points of the autonomous system. We also find four scaling attractor solutions with the property that the ratio of dark energy to dark matter density parameters are of order one. These solutions give the hope to alleviate the well-known coincidence problem in cosmology.

Dynamical system analysis of Hessence scalar field in teleparallel gravity: Invariant manifold technique

2019 ◽  
Vol 34 (28) ◽  
pp. 1950156 ◽  
Author(s):  
Subhajyoti Pal ◽  
Subenoy Chakraborty
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
Invariant Manifold ◽  
Critical Points ◽  
System Analysis ◽  
Teleparallel Gravity ◽  
Center Manifolds ◽  
Field Equations ◽  
Stability Diagrams ◽  
Nonlinear Autonomous System

This paper investigates the cosmological dynamics of the Hessence scalar field coupled with the dark matter in the background of the teleparallel gravity. We have assumed that the potential of the scalar field is exponential in nature whereas the [Formula: see text] appearing in the teleparallel theory has the form [Formula: see text]. The field equations of this system reduce to a nonlinear autonomous system and dynamical system analysis is then performed. Due to the nonlinearity and the existence of multiple zero eigenvalues, the traditional procedures of analysis break down. So some novel technique is required. One of the latest such techniques is the invariant manifold theory. By the application of this theory, one projects the variables linked with the zero eigenvalues onto the variables linked with the nonzero eigenvalues to compute the center manifolds and the reduced systems associated with the critical points. These reduced systems reflect the nature of the whole dynamical systems. They also have less dimension and are often simple in nature. Hence, it is possible to solve them directly. In this paper, we work exactly in this spirit and find the center manifolds and solve the corresponding reduced system for some of the critical points associated with the dynamical system. We discover some interesting results namely that there are certain bounds on the interaction term [Formula: see text] which asserts the stability of the systems. We also present various stability diagrams of the reduced systems. An asymptotic analysis is then done for the critical points at infinity. Finally, we discuss the cosmological interpretation of our results.

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