scholarly journals Dynamical System Analysis of Interacting Hessence Dark Energy inf(T)Gravity

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Jyotirmay Das Mandal ◽  
Ujjal Debnath
Keyword(s):  
Dynamical System ◽  
Autonomous System ◽  
System Analysis ◽  
Nonlinear Dynamical System ◽  
Computational Method ◽  
Dynamical Analysis ◽  
Dynamical System Theory ◽  
Nonlinear Dynamical ◽  
The Stability ◽  
The Universe

We have carried out dynamical system analysis of hessence field coupling with dark matter inf(T)gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is nonlinear. So, we have applied the theory of nonlinear dynamical system. We have noticed that very few papers are devoted to this kind of study. Maximum works in literature are done treating the dynamical system as done in linear dynamical analysis, which are unable to predict correct evolution. Our work is totally different from those kinds of works. We have used nonlinear dynamical system theory, developed till date, in our analysis. This approach gives totally different stable solutions, in contrast to what the linear analysis would have predicted. We have discussed the stability analysis in detail due to exponential potential through computational method in tabular form and analysed the evolution of the universe. Some plots are drawn to investigate the behaviour of the system(this plotting technique is different from usual phase plot and that devised by us). Interestingly, the analysis shows that the universe may resemble the “cosmological constant” like evolution (i.e.,ΛCDM model is a subset of the solution set). Also, all the fixed points of our model are able to avoid Big Rip singularity.

scholarly journals Dynamical analysis of autonomous system in entropic cosmology

2016 ◽  
Vol 94 (5) ◽  
pp. 458-465
Author(s):  
Yu Li
Keyword(s):  
Fixed Points ◽  
Autonomous System ◽  
Constant Term ◽  
Accelerated Expansion ◽  
Dynamical Analysis ◽  
Stability Properties ◽  
Expansion Of The Universe ◽  
Dynamical Properties ◽  
The Stability ◽  
The Universe

The entropic cosmology model is an alternative method to explain the accelerated expansion of the universe. In this paper, we discuss the dynamical system in two types of entropic cosmology model: Λ(t) type and bulk viscous type. We found that the stability properties of fixed points are affected by the H2 term, while the H term and constant term have no influence on stability properties of fixed points. We also found that the dynamical properties of the C-version model are the same as the H-version model.

Jacobi stability analysis of Rikitake system

2016 ◽  
Vol 13 (07) ◽  
pp. 1650098 ◽  
Author(s):  
M. K. Gupta ◽  
C. K. Yadav
Keyword(s):  
Dynamical System ◽  
Differential Geometry ◽  
Stability Analysis ◽  
Nonlinear Differential Equations ◽  
Equilibrium Points ◽  
Nonlinear Dynamical System ◽  
Intrinsic Properties ◽  
Nonlinear Dynamical ◽  
Rikitake System ◽  
The Stability

We study the Rikitake system through the method of differential geometry, i.e. Kosambi–Cartan–Chern (KCC) theory for Jacobi stability analysis. For applying KCC theory we reformulate the Rikitake system as two second-order nonlinear differential equations. The five KCC invariants are obtained which express the intrinsic properties of nonlinear dynamical system. The deviation curvature tensor and its eigenvalues are obtained which determine the stability of the system. Jacobi stability of the equilibrium points is studied and obtain the conditions for stability. We study the dynamics of Rikitake system which shows the chaotic behaviour near the equilibrium points.

scholarly journals On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2057
Author(s):  
Alexander N. Pchelintsev
Keyword(s):  
Dynamical System ◽  
Numerical Method ◽  
High Precision ◽  
Fourth Order ◽  
Nonlinear Dynamical System ◽  
Search Procedure ◽  
Nonlinear Dynamical ◽  
Poisson Stability ◽  
Quadratic Nonlinearities ◽  
The Stability

This article discusses the search procedure for Poincaré recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system, using a previously developed high-precision numerical method. For the resulting limiting solution, the Lyapunov exponents are calculated, using the modified Benettin’s algorithm to study the stability of the found regime and confirm the type of attractor.

NOISE REDUCTION BY GRADIENT DESCENT

1993 ◽  
Vol 03 (01) ◽  
pp. 113-118 ◽  
Author(s):  
MIKE DAVIES
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Gradient Descent ◽  
Nonlinear Dynamical System ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Gradient Descent Method ◽  
Local Minima ◽  
Nonlinear Dynamical ◽  
The Stability

The problem of reducing noise in a time series from a nonlinear dynamical system can be formulated as a nonlinear minimisation process. This paper demonstrates that this can be easily solved using a steepest descent method without any of the stability problems that have been associated with using a Newton method [Hammel, 1990; Farmer & Sidorowich, 1991]. The optimisation function to be minimised is also shown not to contain any local minima if the trajectory is always hyperbolic. So that in this case this method will converge eventually to a purely deterministic trajectory. Finally this method is compared with a recently proposed algorithm [Schreiber & Grassberger, 1991], which can be viewed as an alternative gradient descent method.

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