scholarly journals Chaotic Convection of Viscoelastic Fluid in Porous Medium Under G-Jitter

2019 ◽  
Vol 24 (1) ◽  
pp. 37-51 ◽  
Author(s):  
B.S. Bhadauria ◽  
A. Singh ◽  
M.K. Singh
Keyword(s):  
Viscoelastic Fluid ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Expansion Method ◽  
Suitable Parameter ◽  
Chaotic Convection ◽  
Chaotic Nature ◽  
The Lorenz System ◽  
Parameter Values ◽  
Retardation Parameter

Abstract The present article aims at investigating the effect of gravity modulation on chaotic convection of a viscoelastic fluid in porous media. For this, the problem is reduced into Lorenz system (non-autonomous) by employing the truncated Galerkin expansion method. The system shows transitions from periodic to chaotic behavior on increasing the scaled Rayleigh number R. The amplitude of modulation advances the chaotic nature in the system while the frequency of modulation has a tendency to delay the chaotic behavior which is in good agreement with the results due to [1]. The behavior of the scaled relaxation and retardation parameter on the system is also studied. The phase portrait and time domain diagrams of the Lorenz system for suitable parameter values have been used to analyze the system.

Feedback Control of Chaos in Porous Medium under G-jitter Effects

2018 ◽  
Vol 10 (1) ◽  
Author(s):  
Ajay Singh ◽  
B.S. Bhadauria ◽  
Prashant Kumar Gangwar
Keyword(s):  
Porous Medium ◽  
Feedback Control ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Expansion Method ◽  
Gravity Modulation ◽  
Control Of Chaos ◽  
Chaotic Convection ◽  
Chaotic Nature ◽  
Energy Equations

In the present paper, we studied feedback control of chaotic convection in porous medium under gravity modulation. A non-autonomous system having three differential equations is obtained by employing the truncated Galerkin expansion method in to the modulated momentum and energy equations, called as Lorenz system in the literature. The parameter R demonstrates either periodic or chaotic behavior of the system as increasing R. It is also found that the influence of amplitude of modulation is to advance the chaotic nature in the system whereas the feedback control and frequency of modulation parameters have tendency to delay the chaotic behavior.

Feedback Control of Chaos in Porous Medium under G-jitter Effects

2018 ◽  
Vol 10 (01) ◽  
pp. 25-32
Author(s):  
Ajay Singh ◽  
B. S. Bhadauria ◽  
Prashant Kumar Gangwar
Keyword(s):  
Porous Medium ◽  
Feedback Control ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Expansion Method ◽  
Gravity Modulation ◽  
Control Of Chaos ◽  
Chaotic Convection ◽  
Chaotic Nature ◽  
Energy Equations

In the present paper, we studied feedback control of chaotic convection in porous medium under gravity modulation. A non-autonomous system having three differential equations is obtained by employing the truncated Galerkin expansion method in to the modulated momentum and energy equations, called as Lorenz system in the literature. The parameter R demonstrates either periodic or chaotic behavior of the system as increasing R. It is also found that the influence of amplitude of modulation is to advance the chaotic nature in the system whereas the feedback control and frequency of modulation parameters have tendency to delay the chaotic behavior.

scholarly journals Stability Analysis of the Chaotic Lorenz System with a State-Feedback Controller

2021 ◽  
Author(s):  
Dan Jones
Keyword(s):  
Strange Attractor ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Geometric Approach ◽  
Stable Equilibrium Point ◽  
The Lorenz System ◽  
The Stability ◽  
Parameter Values

The Lorenz model is considered a benchmark system in chaotic dynamics in that it displays extraordinary sensitivity to initial conditions and the strange attractor phenomenon. Even though the system tends to amplify perturbations, it is indeed possible to convert a strange attractor to a non-chaotic one using various control schemes. In this work it is shown that the chaotic behavior of the Lorenz system can be suppressed through the use of a feedback loop driven by a quotient controller. The stability of the controlled Lorenz system is evaluated near its equilibrium points using Routh-Hurwitz testing, and the global stability of the controlled system is established using a geometric approach. It is shown that the controlled Lorenz system has only one globally stable equilibrium point for the set of parameter values under consideration.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Chaos in the Periodically Parametrically Excited Lorenz System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130024
Author(s):  
Weisheng Huang ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Parametrically Excited ◽  
The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

Tangent bundle viewpoint of the Lorenz system and its chaotic behavior

2010 ◽  
Vol 374 (11-12) ◽  
pp. 1315-1319 ◽  
Author(s):  
Takahiro Yajima ◽  
Hiroyuki Nagahama
Keyword(s):  
Tangent Bundle ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
The Lorenz System

COLOR MAP OF LYAPUNOV EXPONENTS OF INVARIANT SETS

1999 ◽  
Vol 09 (07) ◽  
pp. 1459-1463 ◽  
Author(s):  
MARCO MONTI ◽  
WILLIAM B. PARDO ◽  
JONATHAN A. WALKENSTEIN ◽  
EPAMINONDAS ROSA ◽  
CELSO GREBOGI
Keyword(s):  
Lyapunov Exponent ◽  
Parameter Space ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Invariant Sets ◽  
Largest Lyapunov Exponent ◽  
Specific Behavior ◽  
Practical Applications ◽  
The Lorenz System ◽  
Different Levels

The largest Lyapunov exponent of the Lorenz system is used as a measure of chaotic behavior to construct parameter space color maps. Each color in these maps corresponds to different values of the Lyapunov exponent and indicates, in parameter space, the locations of different levels of chaos for the Lorenz system. Practical applications of these maps include moving in parameter space from place to place without leaving a region of specific behavior of the system.

scholarly journals On the topology of the Lorenz system

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170374 ◽  
Author(s):  
Tali Pinsky
Keyword(s):  
Invariant Manifolds ◽  
Lorenz System ◽  
Three Dimensional ◽  
Lorenz Equations ◽  
New Paradigm ◽  
Anosov Flow ◽  
Trefoil Knot ◽  
The Lorenz System ◽  
Parameter Values ◽  
Special Parameter

We present a new paradigm for three-dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension 3 is the existence of singularities. We show how to use knot theory as a way to remove the singularities. Specifically, we claim: (i) for certain parameters, the Lorenz system has an invariant one-dimensional curve, which is a trefoil knot. The knot is a union of invariant manifolds of the singular points. (ii) The flow is topologically equivalent to an Anosov flow on the complement of this curve, and moreover to a geodesic flow. (iii) When varying the parameters, the system exhibits topological phase transitions, i.e. for special parameter values, it will be topologically equivalent to an Anosov flow on a knot complement. Different knots appear for different parameter values and each knot controls the dynamics at nearby parameters.

ANALYSIS ON TOPOLOGICAL PROPERTIES OF THE LORENZ AND THE CHEN ATTRACTORS USING GCM

2007 ◽  
Vol 17 (08) ◽  
pp. 2791-2796 ◽  
Author(s):  
PEI YU ◽  
WEIGUANG YAO ◽  
GUANRON CHEN
Keyword(s):  
Lorenz System ◽  
Point Of View ◽  
Lorenz Attractor ◽  
Topological Properties ◽  
Chen System ◽  
Two Systems ◽  
Typical Parameter ◽  
The Lorenz System ◽  
Parameter Values

This letter reports a study on some topological properties of chaos using a generalized competitive mode (GCM). The Lorenz system and the Chen system are used as examples for comparison. It is shown that for typical parameter values used in the two systems, the Lorenz attractor has one pair of GCMs in competition, while the Chen attractor has two pairs of GCMs in competition. This explains why the two attractors are topologically different, and furthermore indicates that the Chen attractor is more complex than the Lorenz attractor from the dynamics point of view.

A COMMON PHENOMENON IN CHAOTIC SYSTEMS LINKED BY TIME DELAY

2006 ◽  
Vol 16 (12) ◽  
pp. 3727-3736 ◽  
Author(s):  
PEI YU ◽  
FEI XU
Keyword(s):  
Time Delay ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Common Phenomenon ◽  
State Variables ◽  
Chen System ◽  
The Family ◽  
The Lorenz System ◽  
Parameter Values ◽  
Liu System

In this paper, we report a common phenomenon observed in chaotic systems linked by time delay. Recently, the Lorenz chaotic system has been extended to the family of Lorenz systems which includes the Chen and Lü systems. These three chaotic systems, corresponding to different sets of system parameter values, are topologically different. With the aid of numerical simulations, we have surprisingly found that a simple time delay, directly applied to one or more state variables, transforms the Lorenz system to the generalized Chen system or the generalized Lü system without any parameter changes. The existence of this phenomenon has also been found in other known chaotic systems: the Rössler system, the Chua's circuit and the 4-Liu system. This finding has shown a common characteristic of chaotic systems: a new chaotic "branch" can be created from a chaotic attractor by simply adding a time delay.

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