A Chaotic System with Constant Lyapunov Exponent Spectrum and its Evolvement

2010 ◽  
Author(s):  
Chun-Biao Li
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Lyapunov Exponent Spectrum

Realization of a Novel Logarithmic Chaotic System and Its Characteristic Analysis

2019 ◽  
Vol 29 (02) ◽  
pp. 1930004 ◽  
Author(s):  
Xiaoyuan Wang ◽  
Xiaotao Min ◽  
Jun Yu ◽  
Yiran Shen ◽  
Guangyi Wang ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Nonlinear Term ◽  
Experimental Results ◽  
Characteristic Analysis ◽  
Chaotic Parameter ◽  
Hardware Circuit ◽  
Lyapunov Exponent Spectrum

To further improve the complexity of the chaotic system and broaden the chaotic parameter range, a novel logarithmic chaotic system was constructed by adding a nonlinear term of logarithm. The dynamic characteristics of the chaotic system were analyzed by chaotic phase diagram, bifurcation diagram, Lyapunov exponent spectrum, Poincaré mapping and dynamical map, etc. The system was digitized by DSP simulation, and the corresponding experimental results are completely consistent with the theoretical analysis. Furthermore, the equivalent hardware circuit was designed and theoretical analysis was verified by its experimental results.

scholarly journals Symmetric Coexisting Attractors in a Novel Memristors-Based Chuas Chaotic System

2021 ◽  
Author(s):  
Shaohui Yan ◽  
Zhenlong Song ◽  
Wanlin Shi
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Analog Circuits ◽  
Complex Dynamics ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Initial Value ◽  
Field Programmable ◽  
A Charge ◽  
Lyapunov Exponent Spectrum

This paper introduces a charge-controlled memristor based on the classical Chuas circuit. It also designs a novel four-dimensional chaotic system and investigates its complex dynamics, including phase portrait, Lyapunov exponent spectrum, bifurcation diagram, equilibrium point, dissipation and stability. The system appears as single-wing, double-wings chaotic attractors and the Lyapunov exponent spectrum of the system is symmetric with respect to the initial value. In addition, symmetric and asymmetric coexisting attractors are generated by changing the initial value and parameters. The findings indicate that the circuit system is equipped with excellent multi-stability. Finally, the circuit is implemented in Field Programmable Gate Array (FPGA) and analog circuits.

scholarly journals A novel chaotic system and its topological horseshoe

2013 ◽  
Vol 18 (1) ◽  
pp. 66-77 ◽  
Author(s):  
Chunlai Li ◽  
Lei Wu ◽  
Hongmin Li ◽  
Yaonan Tong
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Signal Amplitude ◽  
Topological Horseshoe ◽  
Lorenz Chaotic System ◽  
Construction Pattern ◽  
Lyapunov Exponent Spectrum

Based on the construction pattern of Chen, Liu and Qi chaotic systems, a new threedimensional (3D) chaotic system is proposed by developing Lorenz chaotic system. It’s found that when parameter e varies, the Lyapunov exponent spectrum keeps invariable, and the signal amplitude can be controlled by adjusting e. Moreover, the horseshoe chaos in this system is investigated based on the topological horseshoe theory.

A Image Transmission System Based on Logistic Map

2012 ◽  
Vol 468-471 ◽  
pp. 727-732 ◽  
Author(s):  
Zhang Gang ◽  
Li Fang He ◽  
Tian Qi Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Communication System ◽  
Logistic Map ◽  
Image Transmission ◽  
Chaotic Synchronization ◽  
Synchronization System ◽  
Simulation Results ◽  
Chaotic Parameter ◽  
Lyapunov Exponent Spectrum

A method for chaotic synchronization system based on nonlinear control was studied. The general approach to chaotic system is following Logistic map. First, the parameter which meets chaotic status was analyzed and found via bifurcation diagram and Lyapunov exponent spectrum. The system can be synchronized quickly after just only a single iteration. Then, the method of implementing the synchronization system within a chaotic parameter modulation based communication system was researched. The deduction and simulation results also showed the probability for implementation the system in fast secure chaotic communications that require instant synchronization schemes. Finally, the chaotic system was applied in image transmission and the simulation results were also given.

scholarly journals Comparison of Complexity of the Switchable Chaotic Systems and its FPGA Implementation

2021 ◽  
Author(s):  
Shaohui Yan ◽  
Qiyu Wang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Order System ◽  
Integer Order ◽  
Coexistence Of Attractors ◽  
Field Programmable ◽  
Lyapunov Exponent Spectrum

Abstract A four-dimensional chaotic system with complex dynamical properties is constructed via introducing a nonlinear function term. The paper assesses complexity of the system employing equilibrium points, Lyapunov exponent spectrum and bifurcation model. Specially, the coexisting Lyapunov exponent spectrum and the coexisting bifurcation validate the coexistence of attractors. The corresponding complexity characteristics of the system can be analyzed by using C0 and spectral entropy(SE) complexity algorithms, and the most complicated integer-order system is obtained. Furthermore, the circuit which can switch the chaotic attractors is implemented. It is worth noting that the more sophisticated parameters are received by comparing the complexity of the most complicated integer-order chaotic system with corresponding fractional-order chaotic system. Finally, the results of simulation model built in the MATLAB are the same as the hardware verified on the Field-Programmable Gate Array(FPGA) platform, which verify the feasibility of the system.

Study on State Recognition of ASCE Benchmark Based on Lyapunov Exponent Spectrum Entropy

2011 ◽  
Vol 243-249 ◽  
pp. 5435-5439 ◽  
Author(s):  
Jian Xi Yang ◽  
Jian Ting Zhou ◽  
Yue Chen
Keyword(s):  
Lyapunov Exponent ◽  
Time Sequence ◽  
Maximum Lyapunov Exponent ◽  
Entropy Analysis ◽  
Structural System ◽  
Time Duration ◽  
State Recognition ◽  
Chaotic Characteristic ◽  
Lyapunov Exponent Spectrum ◽  
Maximum Lyapunov Exponents

The paper has made a maximum Lyapunov exponent and Lyapunov exponent spectrum entropy analysis of ASCE Benchmark using non-linear theory and chaos time sequence. The maximum Lyapunov exponents in the two kinds of structural monitored data are both over zero, indicating that in the structural system chaos phenomenon has appeared. And, experiments have shown that the maximum Lyapunov exponent is sensitive of the amount of samples and the time delay. So, to compute the chaos index, the amount of samples and the time duration are of importance. Meanwhile, the Lyapunov exponent spectrum entropy is effective to measure the chaotic characteristic of the system, but ,the entropy is less sensitive to state recognition more than the max Lyapunov exponent.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

Sign in / Sign up

Export Citation Format

Share Document