A NEW CHAOTIC SYSTEM AND CONTROL

2007 ◽  
Vol 21 (25) ◽  
pp. 1687-1696 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU ◽  
YAHUI LANG
Keyword(s):  
Fractal Dimension ◽  
Chaotic System ◽  
Hyperbolic Function ◽  
Control Methods ◽  
Chen System ◽  
New Chaotic System ◽  
Unstable Equilibrium Point ◽  
Dynamical Properties ◽  
Conditions Of Stability ◽  
And Control

In this paper a chaotic system is proposed via modifying hyperchaotic Chen system. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic behaviors of this system are studied. The conventional feedback, linear function feedback, nonlinear hyperbolic function feedback control methods are applied to control chaos to unstable equilibrium point. The conditions of stability to control the system is derived according to the Routh–Hurwitz criteria. Numerical results have shown the validity of the proposed schemes.

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.

scholarly journals Generation of a New Three Dimension Autonomous Chaotic Attractor and its Four Wing Type

2013 ◽  
Vol 3 (1) ◽  
pp. 352-358
Author(s):  
F. Yu ◽  
C. Wang
Keyword(s):  
Fractal Dimension ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Topological Structure ◽  
Nonlinear Term ◽  
Chaotic Attractors ◽  
Three Dimension ◽  
Hyperbolic Sine ◽  
New Chaotic System ◽  
Dynamical Properties

In this paper, a new three-dimension (3D) autonomous chaotic system with a nonlinear term in the form of a hyperbolic sine (or cosine) function is reported. Some interesting and complex attractors are obtained. Basic dynamical properties of the new chaotic system are demonstrated in terms of Lyapunov exponents, Poincare mapping, fractal dimension and continuous spectrum. Meanwhile, for further enhancing the complexity of the topological structure of the new chaotic attractors, the attractors are changed from two-wing to four-wing through making axis doubly polarized, theoretically analyzed and numerically simulated. The obtained results clearly show that the chaotic system deserves further detailed investigation.

HYPERCHAOS GENERATED FROM THE UNIFIED CHAOTIC SYSTEM AND ITS CONTROL

2010 ◽  
Vol 24 (23) ◽  
pp. 4619-4637 ◽  
Author(s):  
XING-YUAN WANG ◽  
GUO-BIN ZHAO
Keyword(s):  
Tracking Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Hyperbolic Function ◽  
Hyperchaotic System ◽  
Control Methods ◽  
Third Order ◽  
Unified Chaotic System ◽  
Unstable Equilibrium Point ◽  
New Hyperchaotic System

In this paper, a new hyperchaotic system is formulated by introducing an additional state into the third-order unified system. Some of its basic dynamical properties, such as Lyapunov exponent, bifurcation diagram and the Poincáre section are investigated. It was found that the system is hyperchaotic in several different regions of the parameters. The analysis of equilibrium points and stability are also given. Two different methods, i.e., nonlinear hyperbolic function feedback control and tracking control methods, are used to control hyperchaos in the new hyperchaotic system. Based on the Routh–Hurwitz criteria, the conditions suppressing hyperchaos to unstable equilibrium point are discussed. A tracking control method is proposed. It is also proved that the strategy can make the system approach any desired smooth orbit at an exponential rate. Numerical results have shown the effectiveness of the control methods.

A New Autonomous Chaotic System and its Circuit Simulation

2014 ◽  
Vol 986-987 ◽  
pp. 1726-1729
Author(s):  
Heng Chen ◽  
Teng Fei Lei ◽  
Jing Meng ◽  
Rong Wang
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Signal Detection ◽  
Chaotic System ◽  
Circuit Simulation ◽  
Heteroclinic Orbit ◽  
Secure Communications ◽  
Weak Signal ◽  
Weak Signal Detection ◽  
New Chaotic System

In this paper, a new chaotic system is constructed. This system contains four parameters and two nonlinear terms. The fractal dimension and the heteroclinic orbit are analyzed in the system. Meanwhile, the circuit of the chaotic system is designed by using Mutisim software. The conclusion confirms the consistency of the numerical simulation and circuit. Because of the above properties, the proposed system has a wide application in such as weak signal detection secure communications and secure communications.

A New Chaotic System Family Dynamics Analysis and Circuit Implementation

2013 ◽  
Vol 392 ◽  
pp. 232-236
Author(s):  
Shu Min Duan ◽  
Guo Zeng Wu
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Physical Phenomenon ◽  
Three Dimensional ◽  
Dynamics Analysis ◽  
Circuit Implementation ◽  
Parallel Lines ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new three-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation. It is new physical phenomenon that the Poincaré mapping of this system is a group of parallel lines.

A New Imprisoned Strange Attractor

2019 ◽  
Vol 29 (13) ◽  
pp. 1950181
Author(s):  
Fahimeh Nazarimehr ◽  
Viet-Thanh Pham ◽  
Karthikeyan Rajagopal ◽  
Fawaz E. Alsaadi ◽  
Tasawar Hayat ◽  
...  
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Strange Attractor ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Spherical Coordinate ◽  
New Chaotic System ◽  
Route To Chaos ◽  
Dynamical Properties

This paper proposes a new chaotic system with a specific attractor which is bounded in a sphere. The system is offered in the spherical coordinate. Dynamical properties of the system are investigated in this paper. The system shows multistability, and all of its attractors are inside or on the surface of the specific sphere. Bifurcation diagram of the system displays an inverse period-doubling route to chaos. Lyapunov exponents of the system are studied to show its chaotic attractors and predict its bifurcation points.

From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium

2017 ◽  
Vol 27 (06) ◽  
pp. 1750097 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Xiong Wang ◽  
Sajad Jafari ◽  
Christos Volos ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Stable Equilibrium ◽  
Hidden Attractors ◽  
Chen System ◽  
State Variable ◽  
New Chaotic System

Wang–Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium.

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