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.

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.

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.

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.

Some New Dissipative Chaotic Systems with Cyclic Symmetry

2018 ◽  
Vol 28 (13) ◽  
pp. 1850164 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Shirin Panahi ◽  
Anitha Karthikeyan ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Cyclic Symmetry ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Basin Of Attraction

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited. Finally, the circuit implementation is carried out to show their feasibility.

Design and Impelemation of Two Switchable Chaotic Systems

2011 ◽  
Vol 217-218 ◽  
pp. 1725-1728
Author(s):  
Wei Fan ◽  
Zhong Lin Wang ◽  
Ming Qing Xu ◽  
Ai Feng Wang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Lyapunov Dimension ◽  
New Chaotic System

A new chaotic system is built which is consists of two subsystems. A subsystem is analyzed such as equilibrium, eigenvalue, Lyapunov, dimension and Lyapunov exponent. A practical circuit is designed to realize the system and the experimentation is carried out. The manifold chaotic attractor of the two subsystems is observed in the oscillograph, it is good agree with simulation.

scholarly journals Chaos Control and Synchronization via Switched Output Control Strategy

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su ◽  
Yanhui Zeng
Keyword(s):  
Chaotic System ◽  
Control Strategy ◽  
Chaos Control ◽  
Chaotic Systems ◽  
State Variables ◽  
Output Control ◽  
Lorenz Chaotic System ◽  
Control And Synchronization ◽  
Theoretical Results

This paper investigates the control and synchronization of a class of chaotic systems with switched output which is assumed to be switched between the first and the second state variables of chaotic system. Some novel and yet simple criteria for the control and synchronization of a class of chaotic systems are proposed via the switched output. The generalized Lorenz chaotic system is taken as an example to show the feasibility and efficiency of theoretical 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 Parallel multi-layer selector S-Box based on lorenz chaotic system with FPGA implementation

2020 ◽  
Vol 19 (2) ◽  
pp. 784
Author(s):  
Mohamed Saber ◽  
Esam Hagras
Keyword(s):  
Power Consumption ◽  
Chaotic System ◽  
High Speed ◽  
Computational Models ◽  
Chaotic Systems ◽  
Fpga Implementation ◽  
Differential Probability ◽  
Substitution Boxes ◽  
Lorenz Chaotic System ◽  
Hidden Data

<p><span>The substitution box (S-Box) is the main block in the encryption system, which replaces the non-encrypted data by dynamic secure and hidden data. S-Box can be designed based on complex nonlinear chaotic systems that presented in recent papers as a chaotic S-Box. The hardware implementation of these chaotic systems suffers from long processing time (low speed), and high-power consumption since it requires a large number of non-linear computational models. In this paper, we present a high-speed FPGA implementation of Parallel Multi-Layer Selector Substitution Boxes based on the Lorenz Chaotic System (PMLS S-Box). The proposed PMLS chaotic S-Box is modeled using Xilinx System Generator (XSG) in 32 bits fixed-point format, and the architecture implemented into Xilinx Spartan-6 X6SLX45 board. The maximum frequency of the proposed PMLS chaotic S-Box is 381.764 MHz, with dissipates of 77 mwatt. Compared to other S-Box chaotic systems, the proposed one achieves a higher frequency and lower power consumption. In addition, the proposed PMLS chaotic S-Box is analyzed based on S-Box standard tests such as; Bijectivity property, nonlinearity, strict avalanche criterion, differential probability, and bits independent criterion. The five different standard results for the proposed S-Box indicate that PMLSC can effectively resist crypto-analysis attacks, and is suitable for secure communications.</span></p>

scholarly journals On the Caputo-Fabrizio fractal fractional representation for the Lorenz chaotic system

2021 ◽  
Vol 6 (11) ◽  
pp. 12395-12421
Author(s):  
Anastacia Dlamini ◽  
◽  
Emile F. Doungmo Goufo ◽  
Melusi Khumalo
Keyword(s):  
Chaotic System ◽  
Fractional Derivatives ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Integral Operators ◽  
Fractional Dimension ◽  
Science And Engineering ◽  
Widespread Application ◽  
Lorenz Chaotic System

<abstract><p>The widespread application of chaotic dynamical systems in different fields of science and engineering has attracted the attention of many researchers. Hence, understanding and capturing the complexities and the dynamical behavior of these chaotic systems is essential. The newly proposed fractal-fractional derivative and integral operators have been used in literature to predict the chaotic behavior of some of the attractors. It is argued that putting together the concept of fractional and fractal derivatives can help us understand the existing complexities better since fractional derivatives capture a limited number of problems and on the other side fractal derivatives also capture different kinds of complexities. In this study, we use the newly proposed Caputo-Fabrizio fractal-fractional derivatives and integral operators to capture and predict the behavior of the Lorenz chaotic system for different values of the fractional dimension $ q $ and the fractal dimension $ k $. We will look at the well-posedness of the solution. For the effect of the Caputo-Fabrizio fractal-fractional derivatives operator on the behavior, we present the numerical scheme to study the graphical numerical solution for different values of $ q $ and $ k $.</p></abstract>

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