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 An Integer-Order Memristive System with Two- to Four-Scroll Chaotic Attractors and Its Fractional-Order Version with a Coexisting Chaotic Attractor

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Zhou ◽  
Meihua Ke
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Integer Order ◽  
Memristive System ◽  
Lyapunov Exponent Spectrum

First, based on a linear passive capacitor C, a linear passive inductor L, an active-charge-controlled memristor, and a fourth-degree polynomial function determined by charge, an integer-order memristive system is suggested. The proposed integer-order memristive system can generate two-scroll, three-scroll, and four-scroll chaotic attractors. The complex dynamics behaviors are investigated numerically. The Lyapunov exponent spectrum with respect to linear passive inductor L and the two-scroll, three-scroll, and four-scroll chaotic attractors are yielded by numerical calculation. Second, based on the integer-order memristive chaotic system with a four-scroll attractor, a fractional-order version memristive system is suggested. The complex dynamics behaviors of its fractional-order version are studied numerically. The largest Lyapunov exponent spectrum with respect to fractional-order p is yielded. The coexisting two kinds of three-scroll chaotic attractors and the coexisting three-scroll and four-scroll chaotic attractors can be found in its fractional-order version.

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.

scholarly journals Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2145
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng ◽  
Lin Fa
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Time Shift ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
Simulation Results ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.

scholarly journals Complex Dynamics of a Novel Chaotic System Based on an Active Memristor

Electronics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 410 ◽  
Author(s):  
Qinghai Song ◽  
Hui Chang ◽  
Yuxia Li
Keyword(s):  
Signal Processing ◽  
Complex Dynamics ◽  
Digital Signal ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
State Switching ◽  
Autonomous Differential Equations

On the basis of the bistable bi-local active memristor (BBAM), an active memristor (AM) and its emulator were designed, and the characteristic fingerprints of the memristor were found under the applied periodic voltage. A memristor-based chaotic circuit was constructed, whose corresponding dynamics system was described by the 4-D autonomous differential equations. Complex dynamics behaviors, including chaos, transient chaos, heterogeneous coexisting attractors, and state-switches of the system were analyzed and explored by using Lyapunov exponents, bifurcation diagrams, phase diagrams, and Poincaré mapping, among others. In particular, a novel exotic chaotic attractor of the system was observed, as well as the singular state-switching between point attractors and chaotic attractors. The results of the theoretical analysis were verified by both circuit experiments and digital signal processing (DSP) technology.

scholarly journals A Multiscroll Chaotic Attractors with Arrangement of Saddle-Shapes and Its Field Programmable Gate Array (FPGA) Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Faqiang Wang ◽  
Yufang Xiao
Keyword(s):  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Equilibrium Points ◽  
Research Result ◽  
Step Function ◽  
Phase Locked Loops ◽  
Chaotic Attractors ◽  
Digital To Analog Converter ◽  
Field Programmable ◽  
Gate Array

Based on the step function and signum function, a chaotic system which can generate multiscroll chaotic attractors with arrangement of saddle-shapes is proposed and the stability of its equilibrium points is analyzed. The under mechanism for the generation of multiscroll chaotic attractors and the reason for the arrangement of saddle shapes and being symmetric about y-axis are presented, and the rule for controlling the number of scroll chaotic attractors with saddle shapes is designed. Based on the core chips including Altera Cyclone IV EP4CE10F17C8 Field Programmable Gate Array and Digital to Analog Converter chip AD9767, the peripheral circuit and the Verilog Hardware Description Language program for realization of the proposed multiscroll chaotic system is constructed and some experimental results are presented for confirmation. The research result shows that the occupation of multipliers and Phase-Locked Loops in Field Programmable Gate Array is zero.

Generating Multiple Chaotic Attractors from Sprott B System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650177 ◽  
Author(s):  
Qiang Lai ◽  
Shiming Chen
Keyword(s):  
Lyapunov Exponent ◽  
Function Method ◽  
Polynomial Function ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Phenomenon ◽  
Bifurcation Diagrams ◽  
Initial Values ◽  
Index 2 ◽  
Lyapunov Exponent Spectrum

Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear phenomenon, but there are few studies that have previously addressed it to our best knowledge. In this paper, we propose a polynomial function method for generating multiple chaotic attractors from the Sprott B system. The polynomial function extends the number of index-2 saddle foci, which determines the emergence of multiple chaotic attractors in the system. The analysis of the equilibria is presented. Two coexisting chaotic attractors, three coexisting chaotic attractors and four coexisting chaotic attractors are investigated for verifying the effectiveness of the method. The chaotic characteristics of the attractors are shown by bifurcation diagrams, Lyapunov exponent spectrum and phase portraits.

Generating coexisting attractors from a new four-dimensional chaotic system

2020 ◽  
pp. 2150035
Author(s):  
Yan-Mei Hu ◽  
Bang-Cheng Lai
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Linear Functions ◽  
Chaotic Attractors ◽  
Dynamic Evolution ◽  
Coexisting Attractors ◽  
Evolution Analysis ◽  
Fixed Parameter ◽  
Parameter Values ◽  
Multiple Coexisting Attractors

This paper introduces a new four-dimensional chaotic system with a unique unstable equilibrium and multiple coexisting attractors. The dynamic evolution analysis shows that the system concurrently generates two symmetric chaotic attractors for fixed parameter values. Based on this system, an effective method is established to construct an infinite number of coexisting chaotic attractors. It shows that the introduction of some non-linear functions with multiple zeros can increase the equilibria and inspire the generation of coexisting attractor of the system. Numerical simulations verify the availability of the method.

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.

Generation and Circuit Implementation of Multi-Scroll Chaotic Attractors with Controllable Direction

2014 ◽  
Vol 513-517 ◽  
pp. 4559-4562
Author(s):  
Xiao Wen Luo ◽  
Chun Hua Wang
Keyword(s):  
Lyapunov Exponent ◽  
Control Function ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Relative Coefficient ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

An approach for generating multi-scroll chaotic attractors with controllable direction in one plane is proposed. Firstly, an appropriate nonlinear function is selected to control the number and direction of multi-scroll chaotic attractors in the three-order Jerk system. Then, we add new control function to Jerk system and observe Lyapunov exponent spectrum of relative coefficient and the change of equilibrium points. Different multi-scroll chaotic attractors with controllable direction are generated by adjusting the coefficient of the control function in a plane. The implementation of circuit verifies the feasibility of this method.

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