scholarly journals Chen System as a Controlled Weather Model — Physical Principle, Engineering Design and Real Applications

2018 ◽  
Vol 28 (04) ◽  
pp. 1830009 ◽  
Author(s):  
Pitikhate Sooraksa ◽  
Guanrong Chen
Keyword(s):  
Engineering Design ◽  
Time Reversal ◽  
Lorenz System ◽  
Physical Principle ◽  
Indoor Climate ◽  
Chen System ◽  
Weather Model ◽  
Weather Control ◽  
The Lorenz System ◽  
Control Application

This paper presents the Chen system as a controlled weather model. Mathematically, the Chen system is dual to the Lorenz system via time reversal. Physically, the Chen system can be viewed as a controlled weather model from the anti-control perspective. This paper illustrates the physical principle of this controlled weather model, and develops an engineering design of the model for real indoor climate (temperature-humidity) regulation, with a perspective on outdoor weather control application.

Jacobi Stability Analysis of the Chen System

2019 ◽  
Vol 29 (10) ◽  
pp. 1950139 ◽  
Author(s):  
Qiujian Huang ◽  
Aimin Liu ◽  
Yongjian Liu
Keyword(s):  
Periodic Orbit ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chen System ◽  
Nonlinear Connection ◽  
Berwald Connection ◽  
The Lorenz System ◽  
Nonzero Equilibrium ◽  
Deviation Vector

In this paper, the research of the Jacobi stability of the Chen system is performed by using the KCC-theory. By associating a nonlinear connection and a Berwald connection, five geometrical invariants of the Chen system are obtained. The Jacobi stability of the Chen system at equilibrium points and a periodic orbit is investigated in terms of the eigenvalues of the deviation curvature tensor. The obtained results show that the origin is always Jacobi unstable, while the Jacobi stability of the other two nonzero equilibrium points depends on the values of the parameters. And a periodic orbit of the Chen system is proved to be also Jacobi unstable. Furthermore, Jacobi stability regions of the Chen system and the Lorenz system are compared. Finally, the dynamical behavior of the components of the deviation vector near the equilibrium points is also discussed.

HOMOCLINIC AND HETEROCLINIC ORBITS AND BIFURCATIONS OF A NEW LORENZ-TYPE SYSTEM

2011 ◽  
Vol 21 (09) ◽  
pp. 2695-2712 ◽  
Author(s):  
XIANYI LI ◽  
HAIJUN WANG
Keyword(s):  
Chaotic Attractor ◽  
Lorenz System ◽  
Type System ◽  
Pitchfork Bifurcation ◽  
Heteroclinic Orbits ◽  
Chen System ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
The Stability

In this paper, a new Lorenz-type system with chaotic attractor is formulated. The structure of the chaotic attractor in this new system is found to be completely different from that in the Lorenz system or the Chen system or the Lü system, etc., which motivates us to further study in detail its complicated dynamical behaviors, such as the number of its equilibrium, the stability of the hyperbolic and nonhyperbolic equilibrium, the degenerate pitchfork bifurcation, the Hopf bifurcation and the local manifold character, etc., when its parameters vary in their space. The existence or nonexistence of homoclinic and heteroclinic orbits of this system is also rigorously proved. Numerical simulation evidences are also presented to examine the corresponding theoretical analytical results.

Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system

2013 ◽  
Vol 23 (3) ◽  
pp. 033108 ◽  
Author(s):  
Antonio Algaba ◽  
Fernando Fernández-Sánchez ◽  
Manuel Merino ◽  
Alejandro J. Rodríguez-Luis
Keyword(s):  
Lorenz System ◽  
Chen System ◽  
The Lorenz System ◽  
Special Case

Distinguishing Lorenz and Chen Systems Based Upon Hamiltonian Energy Theory

2017 ◽  
Vol 27 (02) ◽  
pp. 1750024 ◽  
Author(s):  
Shijian Cang ◽  
Aiguo Wu ◽  
Zenghui Wang ◽  
Zengqiang Chen
Keyword(s):  
Energy Function ◽  
Lorenz System ◽  
Three Dimensional ◽  
Type System ◽  
Chen System ◽  
First Order ◽  
Dimensional Phase Space ◽  
Ellipsoidal Surface ◽  
Generalized Hamiltonian Realization ◽  
The Lorenz System

Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. Moreover, the energy function and generalized Hamiltonian realization of the Lü system and a four-dimensional hyperchaotic Lorenz-type system are also discussed.

Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method

2012 ◽  
Vol 542-543 ◽  
pp. 1042-1046 ◽  
Author(s):  
Xin Deng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
The Lorenz System ◽  
Lu System

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

When Two Dual Chaotic Systems Shake Hands

2014 ◽  
Vol 24 (06) ◽  
pp. 1450086 ◽  
Author(s):  
J. C. Sprott ◽  
Xiong Wang ◽  
Guanrong Chen
Keyword(s):  
Parameter Space ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Time Variable ◽  
Chen System ◽  
Common Parameter ◽  
The Lorenz System ◽  
The Relationship

This letter reports an interesting finding that the parametric Lorenz system and the parametric Chen system "shake hands" at a particular point of their common parameter space, as the time variable t → +∞ in the Lorenz system while t → -∞ in the Chen system. This helps better clarify and understand the relationship between these two closely related but topologically nonequivalent chaotic systems.

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.

BIFURCATION CONTROL FOR A CLASS OF LORENZ-LIKE SYSTEMS

2011 ◽  
Vol 21 (09) ◽  
pp. 2647-2664 ◽  
Author(s):  
PEI YU ◽  
JINHU LÜ
Keyword(s):  
Lorenz System ◽  
Control Method ◽  
Bifurcation Control ◽  
Equilibrium Solutions ◽  
Chen System ◽  
Feedback Controls ◽  
Chaotic Motions ◽  
The Lorenz System ◽  
The Stability ◽  
Simple Feedback

In this paper, a control method developed earlier is employed to consider controlling bifurcations in a class of Lorenz-like systems. Particular attention is focused on Hopf bifurcation control via linear and nonlinear stability analyses. The Lorenz system, Chen system and Lü system are studied in detail. Simple feedback controls are designed for controlling the stability of equilibrium solutions, limit cycles and chaotic motions. All formulas are derived in general forms including the system parameters. Computer simulation results are presented to confirm the analytical predictions.

scholarly journals Templates of Two Foliated Attractors — Lorenz and Chen Systems

2016 ◽  
Vol 26 (02) ◽  
pp. 1650037
Author(s):  
Martin Rosalie
Keyword(s):  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Lorenz System ◽  
Chen System ◽  
Attractor Solution ◽  
The Lorenz System ◽  
Foliated Structure

A chaotic attractor solution of the Lorenz system [Lorenz, 1963] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [Chen & Ueta, 1999] with a similar foliated structure is also established.

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