scholarly journals NEW COSMOLOGICAL SOLUTIONS AND STABILITY ANALYSIS IN FULL EXTENDED THERMODYNAMICS

1998 ◽  
Vol 07 (02) ◽  
pp. 177-187 ◽  
Author(s):  
LUIS P. CHIMENTO ◽  
ALEJANDRO S. JAKUBI ◽  
VICENÇ MÉNDEZ
Keyword(s):  
Function Method ◽  
De Sitter ◽  
Field Equations ◽  
Full Theory ◽  
New Exact Solutions ◽  
Lyapunov Function Method ◽  
Cosmological Solutions ◽  
Dissipative Fluid ◽  
The Stability ◽  
Nonlocal Transformation

The Einstein's field equations of FRW universes filled with a dissipative fluid described by full theory of causal transport equations are analyzed. New exact solutions are found using a nonlocal transformation on the nonlinear differential equation for the Hubble factor. The stability of the de Sitter and asymptotically Friedmannian solutions are analyzed using Lyapunov function method.

scholarly journals Stability analysis of an interacting holographic dark energy model

2019 ◽  
Vol 34 (19) ◽  
pp. 1950147
Author(s):  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dark Energy ◽  
System Analysis ◽  
Holographic Dark Energy ◽  
Equilibrium Points ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lyapunov Function Method ◽  
Transformation Of Variables ◽  
The Stability ◽  
Manifold Theory

This work deals with dynamical system analysis of Holographic Dark Energy (HDE) cosmological model with different infra-red (IR)-cutoff. By suitable transformation of variables, the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by Center Manifold Theory and Lyapunov function method. Possible bifurcation scenarios have also been explained.

Neuro-Fuzzy Sliding Mode Control of Inverted Pendulum

2013 ◽  
Vol 711 ◽  
pp. 432-439
Author(s):  
Khedoudja Kherraz ◽  
Mustapha Hamerlain ◽  
Nouara Achour
Keyword(s):  
Function Method ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Controller ◽  
Fuzzy Sliding Mode Control ◽  
Neuro Fuzzy ◽  
Lyapunov Function Method ◽  
Fuzzy Sliding Mode ◽  
Simulation Results ◽  
The Stability

In this paper we develop a robust controller based on sliding mode, neural network and fuzzy logic for the control of a class of under-actuated systems. The stability of the proposed controller is proved with the Lyapunov function method. Simulation results are made on an inverted pendulum.

The Stability of the Second-Order Model of the Damping Single Maching Infinite Bus Bar System

2013 ◽  
Vol 457-458 ◽  
pp. 1004-1007
Author(s):  
Hong Ying Luo ◽  
Jun Liu ◽  
Long Xing Li
Keyword(s):  
Lyapunov Function ◽  
Equilibrium Point ◽  
Single Machine ◽  
Function Method ◽  
Second Order ◽  
Order Model ◽  
Lyapunov Function Method ◽  
Single Machine Infinite Bus ◽  
The Stability ◽  
Second Order Model

This paper studies the stability of the second-order model of the damping single machine infinite bus bar system,by constructing a suitable Lyapunov function method,and discuss the stability of the equilibrium point,then obtains the attractive area.

Anisotropic universe and generalized ghost dark energy in Brans–Dicke theory

2016 ◽  
Vol 94 (2) ◽  
pp. 201-208 ◽  
Author(s):  
V. Fayaz ◽  
H. Hossienkhani ◽  
A. Pasqua ◽  
Z. Zarei ◽  
M. Ganji
Keyword(s):  
Dark Energy ◽  
State Parameter ◽  
Anisotropic Universe ◽  
Type I ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Ghost Dark Energy ◽  
The Stability ◽  
Generalized Ghost Dark Energy

In this paper, we consider the generalized ghost dark energy in a Bianchi type-I metric (which is a spatially homogeneous and anisotropic) in the framework of Brans–Dicke theory. For this purpose, we use the squared sound speed [Formula: see text] the sign of which determines the stability of the model. At first, we obtain the equation of state parameter, ωΛ = pΛ/ρΛ, the deceleration parameter q and the evolution equation of the generalized ghost dark energy. We find that, in this case, ωΛ cannot cross the phantom line (ωΛ > –1) and eventually the universe approaches a de-Sitter phase of expansion (ωΛ → –1). Then, we extend our study to the case of generalized ghost dark energy in a non-isotropic and Brans–Dicke framework and find out that the transition of ωΛ to the phantom regime can be more easily accounted for than when it is restored into the Einstein field equations. In conclusion, we find evidence that the generalized ghost dark energy in BD theory can lead to a stable universe favored by observations at the present time.

scholarly journals Damped Perturbations of Systems with Center-Saddle Bifurcation

2021 ◽  
Vol 31 (09) ◽  
pp. 2150137
Author(s):  
Oskar A. Sultanov
Keyword(s):  
Autonomous System ◽  
Function Method ◽  
Critical Case ◽  
The Other ◽  
Unperturbed System ◽  
Driving Frequency ◽  
Bifurcation Parameter ◽  
Perturbed System ◽  
Lyapunov Function Method ◽  
The Stability

An autonomous system of ordinary differential equations on the plane with a center-saddle bifurcation is considered. The influence of a class of time damped perturbations is investigated. The particular solutions tending to the fixed points of the limiting system are considered. The stability of these solutions is analyzed by Lyapunov function method when the bifurcation parameter of the unperturbed system takes critical and noncritical values. Conditions that ensure the persistence of the bifurcation in the perturbed system are described. When the bifurcation is broken, a pair of solutions tending to a degenerate fixed point of the limiting system appears in the critical case. It is shown that, depending on the structure and the parameters of the perturbations, one of these solutions can be stable, metastable or unstable, while the other solution is always unstable. The proposed theory is applied to the study of autoresonance capturing in systems with quadratically varying driving frequency.

Stability analysis of nonlinear impulsive switched positive systems

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanzi Lin ◽  
Ping Zhao
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Function Method ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Positive Systems ◽  
Lyapunov Function Method ◽  
The Stability ◽  
Switched Positive Systems ◽  
Time Linear

Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

Cosmology

2019 ◽  
pp. 92-100
Author(s):  
Steven Carlip
Keyword(s):  
De Sitter Space ◽  
Red Shift ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Cosmological Solutions ◽  
Expansion Of The Universe ◽  
Topology Of The Universe ◽  
The Universe

Starting with the assumptions of homogeneity and isotropy, the cosmological solutions of the Einstein field equations—the Friedmann-Lemaitre-Robertson-Walker metrics—are derived. After a discussion of constant curvature metrics and the topology of the Universe, the chapter moves on to discuss observational implications: expansion of the Universe, cosmological red shift, primordial nucleosynthesis, the cosmic microwave background, and primordial perturbations. The chapter includes a brief discussion of de Sitter and anti-de Sitter space and an introduction to inflation.

Analysis of physically realizable stellar models in embedded class one spacetime manifold

2019 ◽  
Vol 35 (04) ◽  
pp. 2050001 ◽  
Author(s):  
Ritu Tamta ◽  
Pratibha Fuloria
Keyword(s):  
Transverse Velocity ◽  
Compact Star ◽  
Graphical Analysis ◽  
Compact Stars ◽  
Field Equations ◽  
Star Models ◽  
New Exact Solutions ◽  
Spacetime Manifold ◽  
Stellar Models ◽  
The Stability

In this paper, we searched two new exact solutions of Einstein’s field equations for modeling of compact cold stars using embedded class one spacetime continuum. We find out the expressions for pressure, density, anisotropy, redshift, metric potentials and other physical variables in terms of algebraic and trigonometric expressions and observe that all variables show well-behaved trends inside the compact stellar configurations. The causality condition is well maintained by our stellar models, i.e. the radial velocity and transverse velocity are less than l. The stability of our models is assessed via different stability criteria. The Buchdahl condition holds good for our solution. Herrera’s cracking method is applied to check the stability of stellar models. We generate anisotropic compact star models, whose masses and radii are in close agreement with the observed values for compact stars 4U 1538-52, LMCX-4, PSRJ1614-2230. A comparative analysis of the proposed models is carried out based on two different solutions reported in the paper. The appropriate graphical analysis is provided to authenticate the viability of the models.

Sign in / Sign up

Export Citation Format

Share Document