scholarly journals Autonomous dynamical system approach for inflationary Gauss–Bonnet modified gravity

2018 ◽  
Vol 27 (05) ◽  
pp. 1850059 ◽  
Author(s):  
V. K. Oikonomou
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Phase Space ◽  
Modified Gravity ◽  
System Approach ◽  
De Sitter ◽  
Dynamical System Approach ◽  
Independent Variables ◽  
Perfect Fluids ◽  
Autonomous Dynamical System

In this paper, we shall analyze the [Formula: see text] gravity phase space, in the case that the corresponding dynamical system is autonomous. In order to make the dynamical system autonomous, we shall appropriately choose the independent variables, and we shall analyze the evolution of the variables numerically, emphasizing on the inflationary attractors. As we demonstrate, the dynamical system has only one de Sitter fixed point, which is unstable, with the instability being traced in one of the independent variables. This result holds true both in the presence and in the absence of matter and radiation perfect fluids. We argue that this instability could loosely be viewed as an indication of graceful exit in the [Formula: see text] theory of gravity.

A DYNAMICAL SYSTEM APPROACH TO THE GBIG COSMOLOGY

2011 ◽  
Vol 08 (06) ◽  
pp. 1179-1188 ◽  
Author(s):  
KOUROSH NOZARI ◽  
F. KIANI
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Cosmological Constant ◽  
System Approach ◽  
Stable Solution ◽  
Late Time ◽  
Curvature Effect ◽  
De Sitter ◽  
Dynamical System Approach ◽  
Bonnet Term

We study the phase space of an extension of the normal DGP cosmology with a cosmological constant on the brane and curvature effect that is incorporated via the Gauss–Bonnet term in the bulk action. We study late-time cosmological dynamics of this scenario within a dynamical system approach. We show that the stable solution of the cosmological dynamics in this model is a de Sitter phase.

Dynamical system approach for the modified Brans–Dicke theory

2019 ◽  
Vol 28 (10) ◽  
pp. 1950132 ◽  
Author(s):  
Jianbo Lu ◽  
Xin Zhao ◽  
Shining Yang ◽  
Jiachun Li ◽  
Molin Liu
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
Critical Point ◽  
System Approach ◽  
State Parameter ◽  
Kinetic Term ◽  
De Sitter ◽  
Dynamical System Approach ◽  
De Sitter Universe ◽  
Manifold Theory

A modified Brans–Dicke theory (abbreviated as GBD) is proposed by generalizing the Ricci scalar [Formula: see text] to an arbitrary function [Formula: see text] in the original BD action. It can be found that the GBD theory has some interesting properties, such as solving the problem of PPN value without introducing the so-called chameleon mechanism (comparing with the [Formula: see text] modified gravity), making the state parameter to crossover the phantom boundary: [Formula: see text] without introducing the negative kinetic term (comparing with the quintom model). In the GBD theory, the gravitational field equation and the cosmological evolutional equations have been derived. In the framework of cosmology, we apply the dynamical system approach to investigate the stability of the GBD model. A five-variable cosmological dynamical system and three critical points ([Formula: see text], [Formula: see text], [Formula: see text]) are obtained in the GBD model. After calculation, it is shown that the critical point [Formula: see text] corresponds to the radiation dominated universe and it is unstable. The critical point [Formula: see text] is unstable, which corresponds to the geometrical dark energy dominated universe. While for case of [Formula: see text], according to the center manifold theory, this critical point is stable, and it corresponds to geometrical dark energy dominated de Sitter universe ([Formula: see text]).

scholarly journals A fast saddle-point dynamical system approach to robust deep learning

2021 ◽  
Vol 139 ◽  
pp. 33-44
Author(s):  
Yasaman Esfandiari ◽  
Aditya Balu ◽  
Keivan Ebrahimi ◽  
Umesh Vaidya ◽  
Nicola Elia ◽  
...  
Keyword(s):  
Dynamical System ◽  
Deep Learning ◽  
Saddle Point ◽  
System Approach ◽  
Dynamical System Approach

scholarly journals Biometric Palmprint Verification: A Dynamical System Approach

2019 ◽  
Vol 49 (12) ◽  
pp. 2676-2687 ◽  
Author(s):  
David Palma ◽  
Pier Luca Montessoro ◽  
Giulia Giordano ◽  
Franco Blanchini
Keyword(s):  
Dynamical System ◽  
System Approach ◽  
Dynamical System Approach

scholarly journals Autonomous dynamical system description of de Sitter evolution in scalar assisted f(R) − ϕ gravity

2018 ◽  
Vol 15 (12) ◽  
pp. 1850212 ◽  
Author(s):  
K. Kleidis ◽  
V. K. Oikonomou
Keyword(s):  
Dynamical System ◽  
Numerical Analysis ◽  
Scalar Field ◽  
Analysis Approach ◽  
Single Variable ◽  
De Sitter ◽  
Exponential Potential ◽  
System Description ◽  
Variable Formula ◽  
Autonomous Dynamical System

In this paper we will study the cosmological dynamical system of an [Formula: see text] gravity in the presence of a canonical scalar field [Formula: see text] with an exponential potential by constructing the dynamical system in a way that it is rendered autonomous. This feature is controlled by a single variable [Formula: see text], which when it is constant, the dynamical system is autonomous. We focus on the [Formula: see text] case which, as we demonstrate by using a numerical analysis approach, leads to an unstable de Sitter attractor, which occurs after [Formula: see text] [Formula: see text]-foldings. This instability can be viewed as a graceful exit from inflation, which is inherent to the dynamics of de Sitter attractors.

scholarly journals Patterns of Horse-Rider Coordination during Endurance Race: A Dynamical System Approach

PLoS ONE ◽  
2013 ◽  
Vol 8 (8) ◽  
pp. e71804 ◽  
Author(s):  
Sylvain Viry ◽  
Rita Sleimen-Malkoun ◽  
Jean-Jacques Temprado ◽  
Jean-Philippe Frances ◽  
Eric Berton ◽  
...  
Keyword(s):  
Dynamical System ◽  
System Approach ◽  
Dynamical System Approach

The dynamical system approach to scalar field cosmology

2000 ◽  
Vol 17 (8) ◽  
pp. 1783-1814 ◽  
Author(s):  
E Gunzig ◽  
V Faraoni ◽  
A Figueiredo ◽  
T M Rocha Filho ◽  
L Brenig
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
System Approach ◽  
Dynamical System Approach ◽  
Scalar Field Cosmology
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