A dynamical system approach to the holographic dark energy in a modified theory of gravity

2021 ◽  
Author(s):  
Farida Bargach ◽  
Aatifa Bargach ◽  
Ahmed Errahmani ◽  
Mariam Bouhmadi-Lopez ◽  
Taoufik Ouali
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
System Approach ◽  
Holographic Dark Energy ◽  
Dynamical System Approach ◽  
Modified Theory Of Gravity ◽  
Theory Of Gravity ◽  
Modified Theory

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 Interacting agegraphic dark energy model in DGP brane-world cosmology: Dynamical system approach

2019 ◽  
Vol 34 (14) ◽  
pp. 1950105 ◽  
Author(s):  
A. Ravanpak ◽  
G. F. Fadakar
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
System Approach ◽  
Dark Energy Model ◽  
Acoustic Oscillation ◽  
Energy Model ◽  
Brane World ◽  
Model Parameters ◽  
Dynamical System Approach ◽  
Agegraphic Dark Energy

A proposal to study the effect of interaction in an agegraphic dark energy model in DGP brane-world cosmology is presented in this paper. After explaining the details, we proceed to apply the dynamical system approach to the model to analyze its stability. We first constrain model parameters with a variety of independent observational data such as cosmic microwave background anisotropies, baryon acoustic oscillation peaks and observational Hubble data. Then, we obtain the critical points related to different cosmological epochs. In particular, we conclude that in the presence of interaction, dark energy dominated era could be a stable point if model parameters n and [Formula: see text], obey a given constraint. Also, big rip singularity is avoidable in this model.

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
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