Friedmann-like universes with weak torsion: a dynamical system approach

Abstract We consider Friedmann-like universes with torsion and take a step towards studying their stability. In so doing, we apply dynamical-system techniques to an autonomous system of differential equations, which monitors the evolution of these models via the associated density parameters. Assuming relatively weak torsion, we identify the system’s equilibrium points. These are found to represent homogeneous and isotropic spacetimes with nonzero torsion that undergo accelerated expansion. We then examine the linear stability of the aforementioned fixed points. Our results indicate that Friedmann-like cosmologies with weak torsion are generally stable attractors, either asymptotically or in the Lyapunov sense. In addition, depending on the equation of state of the matter, the equilibrium states can also act as intermediate saddle points, marking a transition from a torsional to a torsion-free universe.

Download Full-text

Dynamical system approach to cosmological evolution in modified theories of gravity with coupling between matter and geometry

Modern Physics Letters A ◽

10.1142/s0217732320501540 ◽

2020 ◽

Vol 35 (19) ◽

pp. 2050154

Author(s):

Jun Wang ◽

Kang Liu

Keyword(s):

Dynamical System ◽

System Approach ◽

Cosmic Radiation ◽

Cosmological Evolution ◽

Accelerated Expansion ◽

Modified Theories Of Gravity ◽

Late Time ◽

Dynamical System Approach ◽

Dynamical Approach ◽

Theories Of Gravity

In this paper, a class of [Formula: see text] gravitational models with coupling between matter and geometry have been studied by a dynamical approach in cosmology. The result shows that both the cosmic radiation dominated era and the late-time cosmic accelerated expansion can be achieved in this class of models. Moreover, the corresponding parameters are constrained as well.

Download Full-text

Cosmological dynamics of dark energy in scalar-torsion $$f(T,\phi )$$ gravity

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09270-x ◽

2021 ◽

Vol 81 (5) ◽

Author(s):

Manuel Gonzalez-Espinoza ◽

Giovanni Otalora

Keyword(s):

Dark Energy ◽

Dark Energy Model ◽

Autonomous System ◽

Saddle Points ◽

Teleparallel Gravity ◽

Cosmic Acceleration ◽

Accelerated Expansion ◽

Fluid Density ◽

Exponential Potential ◽

The Stability

AbstractIt is investigated the cosmological dynamics of scalar-torsion $$f(T,\phi )$$ f ( T , ϕ ) gravity as a dark energy model, where T is the torsion scalar of teleparallel gravity and $$\phi $$ ϕ is a canonical scalar field. In this context, we are concerned with the phenomenology of the class of models with non-linear coupling to gravity and exponential potential. We obtain the critical points of the autonomous system, along with the stability conditions of each one of them and their cosmological properties. Particularly, we show the existence of new attractors with accelerated expansion, as well as, new scaling solutions in which the energy density of dark energy scales as the background fluid density, thus, defining the so-called scaling radiation and scaling matter epochs. The scaling solutions are saddle points, and therefore, the system exits these solutions to the current epoch of cosmic acceleration, towards an attractor point describing the dark energy-dominated era.

Download Full-text

MAGNETIZATION DYNAMICS IN FERROFLUIDS: A DYNAMICAL SYSTEM APPROACH

10.26678/abcm.encit2018.cit18-0202 ◽

2018 ◽

Author(s):

Guilherme Hasse Urel ◽

Rafael Gontijo ◽

Francisco Ricardo Cunha

Keyword(s):

Dynamical System ◽

System Approach ◽

Magnetization Dynamics ◽

Dynamical System Approach

Download Full-text

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

Neural Networks ◽

10.1016/j.neunet.2021.02.021 ◽

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

Download Full-text

Biometric Palmprint Verification: A Dynamical System Approach

IEEE Transactions on Systems Man and Cybernetics Systems ◽

10.1109/tsmc.2017.2771232 ◽

2019 ◽

Vol 49 (12) ◽

pp. 2676-2687 ◽

Cited By ~ 9

Author(s):

David Palma ◽

Pier Luca Montessoro ◽

Giulia Giordano ◽

Franco Blanchini

Keyword(s):

Dynamical System ◽

System Approach ◽

Dynamical System Approach

Download Full-text

Slow–Fast Behaviors and Their Mechanism in a Periodically Excited Dynamical System with Double Hopf Bifurcations

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421300226 ◽

2021 ◽

Vol 31 (08) ◽

pp. 2130022

Author(s):

Miaorong Zhang ◽

Xiaofang Zhang ◽

Qinsheng Bi

Keyword(s):

Dynamical System ◽

Hopf Bifurcation ◽

Frequency Domain ◽

Autonomous System ◽

Single Mode ◽

Phase Portraits ◽

Hopf Bifurcations ◽

Double Hopf Bifurcation ◽

Exciting Frequency ◽

Slow Passage

This paper focuses on the influence of two scales in the frequency domain on the behaviors of a typical dynamical system with a double Hopf bifurcation. By introducing an external periodic excitation to the normal form of the vector field with double Hopf bifurcation at the origin and taking the exciting frequency far less than the natural frequency, a theoretical model with two scales in the frequency domain is established. Regarding the whole exciting term as a slow-varying parameter leads to a generalized autonomous system, in which the equilibrium branches and their bifurcations with the variation of the slow-varying parameter can be derived. With the increase of the exciting amplitude, different types of bifurcations may be involved in the generalized autonomous system, resulting in several qualitatively different forms of bursting attractors, the mechanism of which is presented by overlapping the transformed phase portraits and the bifurcations of the equilibrium branches. It is found that the single mode 2D torus may evolve to the bursting attractors with mixed modes, in which the trajectory alternates between the single mode oscillations and the mixed mode oscillations. Furthermore, the transitions between the quiescent states and the spiking states may not occur exactly at the bifurcation points because of the slow passage effect, while Hopf bifurcations may cause different forms of repetitive spiking oscillations.

Download Full-text

A Dynamical System Approach to Quantum Mechanics with Imaginary Time

Information Dynamics - NATO ASI Series ◽

10.1007/978-1-4899-2305-9_25 ◽

1991 ◽

pp. 303-309 ◽

Cited By ~ 1

Author(s):

Christian Beck

Keyword(s):

Dynamical System ◽

Quantum Mechanics ◽

System Approach ◽

Imaginary Time ◽

Dynamical System Approach

Download Full-text

Memory Dynamics in Attractor Networks

Computational Intelligence and Neuroscience ◽

10.1155/2015/191745 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Guoqi Li ◽

Kiruthika Ramanathan ◽

Ning Ning ◽

Luping Shi ◽

Changyun Wen

Keyword(s):

Energy Function ◽

Stable Equilibrium ◽

Equilibrium Points ◽

Saddle Points ◽

Memory Systems ◽

Initial Stimulus ◽

Attractor Network ◽

Local Maxima ◽

Attractor Networks ◽

New Energy

As can be represented by neurons and their synaptic connections, attractor networks are widely believed to underlie biological memory systems and have been used extensively in recent years to model the storage and retrieval process of memory. In this paper, we propose a new energy function, which is nonnegative and attains zero values only at the desired memory patterns. An attractor network is designed based on the proposed energy function. It is shown that the desired memory patterns are stored as the stable equilibrium points of the attractor network. To retrieve a memory pattern, an initial stimulus input is presented to the network, and its states converge to one of stable equilibrium points. Consequently, the existence of the spurious points, that is, local maxima, saddle points, or other local minima which are undesired memory patterns, can be avoided. The simulation results show the effectiveness of the proposed method.

Download Full-text