Accuracy Tests on Built-In Algorithms Applied to the Lorenz System

2019 ◽  
Vol 16 (10) ◽  
pp. 4064-4071
Author(s):  
T. O. Tong ◽  
M. C. Kekana ◽  
M. Y. Shatalov ◽  
S. P. Moshokoa
Keyword(s):  
Analytical Solution ◽  
Chaotic System ◽  
Lorenz System ◽  
Black Box ◽  
Numerical Results ◽  
Adams Method ◽  
Residual Functions ◽  
Runge Kutta ◽  
The Lorenz System

This work investigate, An idea of checking accuracy of algorithms from mathematical black box by means of residual functions. Lorenz system is used as case study as the chaotic system does not have analytical solution. The numerical procedures examined include BDF, Adams method and Implicit Runge Kutta methods. The interval of numerical results is t ∈ [0; 10].

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.

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.

COMMUNICATION BETWEEN SYNCHRONIZED RANDOM NUMBER GENERATORS

2004 ◽  
Vol 14 (11) ◽  
pp. 3995-4008 ◽  
Author(s):  
WEIGUANG YAO ◽  
PEI YU ◽  
CHRISTOPHER ESSEX
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Random Number ◽  
Lorenz System ◽  
Random Number Generator ◽  
Number Generator ◽  
Random Number Generators ◽  
The Lorenz System ◽  
Chaotic Carrier

In most published chaos-based communication schemes, the system's parameters used as a key could be intelligently estimated by a cracker based on the fact that information about the key is contained in the chaotic carrier. In this paper, we will show that the least significant digits (LSDs) of a signal from a chaotic system can be so highly random that the system can be used as a random number generator. Secure communication could be built between the synchronized generators nonetheless. The Lorenz system is used as an illustration.

scholarly journals Dynamic Analysis of the Nonlinear Chaotic System with Multistochastic Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Lingling Geng ◽  
Yongguang Yu ◽  
Shuo Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Dynamic Analysis ◽  
Orthogonal Polynomial ◽  
Chaotic System ◽  
Lorenz System ◽  
Deterministic System ◽  
Maximum Lyapunov Exponent ◽  
Nonlinear Chaotic System ◽  
The Lorenz System ◽  
The Given

The nonlinear chaotic system with multistochastic disturbances is investigated. Based on the orthogonal polynomial approximation, the method of transforming the system into an equivalent deterministic system is given. Then dynamic analysis of the nonlinear chaotic system with multistochastic disturbances can be reduced into that of its equivalent deterministic system. Especially, the Lorenz system with multistochastic disturbances is studied to demonstrate the feasibility of the given method. And its dynamic behaviors are gained including the phase portrait, the bifurcation diagram, the Poincaré section, and the maximum Lyapunov exponent.

scholarly journals Realization of a Novel Chaotic System Using Coupling Dual Chaotic System

2021 ◽  
Author(s):  
Salam K. Mousa ◽  
Raied K. Jamal
Keyword(s):  
Time Series ◽  
Chaotic System ◽  
Optical Communications ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Fourier Transforms ◽  
Optical Coupling ◽  
Before And After ◽  
The Lorenz System

Abstract This paper establishes coupling between two various chaotic systems for Lorenz and Rössler circuits. The x-dynamics of Lorenz circuit was coupled numerically with the x dynamics of Rössler circuit. As a result of the optical coupling between these two chaotic systems, it has been observed an exceptional variation in the time series and attractors, which exhibits a novel behavior, leading to a promises method for controlling the chaotic systems. However, performing fast Fourier transforms (FFT) of chaotic dynamics before and after coupling showed an increase in the bandwidth of the Rössler system after its coupling with the Lorenz system, which, in turn increases the possibility of using this system for secure and confidential optical communications.

IMPULSIVE CONTROL OF CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1181-1190 ◽  
Author(s):  
XINZHI LIU ◽  
KOK LAY TEO
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Equilibrium Point ◽  
Chaotic System ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Impulsive Control ◽  
The Lorenz System ◽  
Impulsive Stabilization

This paper studies an impulsive control problem. By utilizing the method of Lyapunov functions, a set of impulsive stabilization criteria are established. These results are then applied to the Lorenz system. It is shown that by using impulsive feedback control, all the solutions of the Lorenz system will converge to an equilibrium point.

ROBUSTNESS AND SIGNAL RECOVERY IN A SYNCHRONIZED CHAOTIC SYSTEM

1993 ◽  
Vol 03 (06) ◽  
pp. 1629-1638 ◽  
Author(s):  
KEVIN M. CUOMO ◽  
ALAN V. OPPENHEIM ◽  
STEVEN H. STROGATZ
Keyword(s):  
Analytical Model ◽  
Chaotic System ◽  
Lorenz System ◽  
Chaotic Signal ◽  
Synchronization Error ◽  
Signal Recovery ◽  
Additive Perturbation ◽  
The Lorenz System

Recent papers have demonstrated that synchronization in the Lorenz system is highly robust to additive perturbation of the drive signal. This property has led to a concept known as chaotic signal masking and recovery. This paper presents experiments and an approximate analytical model that quantify and explain the observed robustness of synchronization in the Lorenz system. In particular, we explain why speech and other narrowband perturbations can be recovered faithfully, even though the synchronization error is comparable in power to the message itself.

BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM

2002 ◽  
Vol 12 (12) ◽  
pp. 2917-2926 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG ◽  
SERGEJ CELIKOVSKY
Keyword(s):  
Chaotic System ◽  
System Parameter ◽  
Lorenz System ◽  
Dual Systems ◽  
Chen System ◽  
Entire Spectrum ◽  
Unified Chaotic System ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
New System

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

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