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.

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.

Circuit Design Contains a Class of Squared Term Lorenz Family Chaotic System

2014 ◽  
Vol 602-605 ◽  
pp. 2684-2687
Author(s):  
Yu Zhang ◽  
Chong Lou Tong ◽  
Teng Fei Lei
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Circuit Design ◽  
Chaotic System ◽  
Lorenz System ◽  
Three Dimensional ◽  
System Stability ◽  
Experimental Simulation ◽  
Chaotic Circuit ◽  
New Class

A new class of three-dimensional chaotic system is constructed by algebraic methods, which has a similar structure with the classic Lorenz system but contains the square term. The equilibrium point of the system stability is analyzed, and the numerical simulation is carried on the bifurcation diagram and Lyapunov exponent. The chaotic circuit of these systems is designed by using the software of EWB. The results of the experimental simulation verify the existence of the chaotic attractor, which provides theoretical reference to the application of such system.

scholarly journals Quantifying local predictability of the Lorenz system using the nonlinear local Lyapunov exponent

2017 ◽  
Vol 10 (5) ◽  
pp. 372-378 ◽  
Author(s):  
Xiao-Wei HUAI ◽  
Jian-Ping LI ◽  
Rui-Qiang DING ◽  
Jie FENG ◽  
De-Qiang LIU
Keyword(s):  
Lyapunov Exponent ◽  
Lorenz System ◽  
Local Lyapunov Exponent ◽  
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.

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.

Application of Indicators for Chaos in Chaotic Circuit Systems

2016 ◽  
Vol 26 (11) ◽  
pp. 1650182 ◽  
Author(s):  
Da-Zhu Ma ◽  
Zhi-Chao Long ◽  
Yu Zhu
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Experiments ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Threshold Values ◽  
Chaotic Circuit ◽  
Qualitative Properties ◽  
Regular Motion ◽  
Fast Lyapunov Indicator ◽  
The Lorenz System

Lyapunov exponent (LE), fast Lyapunov indicator (FLI), relative finite-time Lyapunov indicator (RLI), smaller alignment index (SALI), and generalized alignment index (GALI) are some of the available methods in most conservative systems. This study focuses on the effects of the above indicators on dissipative chaotic circuit systems such as the Lorenz system and a hyperchaotic model. Numerical experiments show that the performances of the chaos indicators in the hyperchaotic system are almost similar to those in the Lorenz system. These indicators clearly provide transition from chaotic to regular motion. However, FLI, RLI, SALI, and GALI cannot describe transition from chaos to hyperchaos. These indicators are also applied to study a new four-dimensional chaotic circuit system. The basic dynamic behaviors and structures are investigated analytically and numerically. The dynamic qualitative properties of individual orbits are observed using an oscilloscope. Moreover, the entire set of LE about the parameter is found to have three threshold values. Comparisons show that all chaos indicators are able to capture chaotic and periodic motion in chaotic circuit systems, but SALI displays significantly different behavior in several periodic orbits. SALI drops exponentially to zero for “morphologically regular” orbits that are actually unstable and sensitive to perturbation. This conclusion can also be confirmed by GALI.

A Novel Four-Order Chaotic System with N-Attractor Multi-Direction Multi-Scroll Attractors

2014 ◽  
Vol 678 ◽  
pp. 81-88
Author(s):  
Wen Shuang Yin ◽  
Dai Jun Wei ◽  
Shi Qiang Chen
Keyword(s):  
Lyapunov Exponent ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
Operational Amplifier ◽  
Experimental Results ◽  
Order System ◽  
Chaotic Attractors ◽  
Maximum Lyapunov Exponent ◽  
Nonlinear Functions ◽  
New System

In this paper, a novel four-order system is proposed. It can generate N-attractor multi-direction multi-scroll attractor by adding simple nonlinear functions. We analyze the new system by using means of maximum Lyapunov exponent, bifurcation diagram and Poincaré maps of the system. Moreover, an minimum operational amplifier circuit is designed for realizing 2×(3×3 ×3) scroll chaotic attractors, and experimental results are also obtained, which verify chaos characteristics of the system.

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.

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].

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