scholarly journals A Simple Parallel Chaotic Circuit Based on Memristor

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 719
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Zhongwei Cui
Keyword(s):  
Time Domain ◽  
Sample Entropy ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Periodic Attractors ◽  
Dynamic Map ◽  
Lyapunov Exponent Spectrum

This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics.

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.

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 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 Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 48
Author(s):  
Hayder Natiq ◽  
Muhammad Rezal Kamel Ariffin ◽  
Muhammad Asyraf Asbullah ◽  
Zahari Mahad ◽  
Mohammed Najah
Keyword(s):  
Power Input ◽  
Sample Entropy ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Stable Model ◽  
Analysis Framework ◽  
Plasma Model ◽  
Pseudorandom Sequences ◽  
Periodic Attractors ◽  
Pellet Injection

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.

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.

A Novel Memristor Chaotic Circuit Based on CFOA

2014 ◽  
Vol 651-653 ◽  
pp. 603-606
Author(s):  
Qing Hui Hong ◽  
Yi Cheng Zeng ◽  
Zhi Jun Li
Keyword(s):  
System Parameter ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Current Feedback ◽  
Op Amp ◽  
Simulation Results ◽  
Lyapunov Exponent Spectrum ◽  
A Current

In this work, we propose a novel memristor chaotic circuit, which is composed of a current feedback op amp (CFOA) and a piecewise-linear memristor. The dynamic properties of the new circuit are demonstrated, such as system dissipation、equilibrium stability、phase portrait、Lyapunov exponent spectrum and bifurcation analysis. Numerical simulation results show that the circuit produces a class of special chaotic attractors. By adjusting the system parameter, the proposed circuit performs chaotic and hyper-chaotic behaviors from inverse doubling-periodic .

Studying the Dynamics and Complexity of a 3D Laser Plasma System

2021 ◽  
Vol 317 ◽  
pp. 556-563
Author(s):  
Muhammad Firdaus Abdul Rahim ◽  
Hayder Natiq ◽  
Nur Aisyah Abdul Fataf
Keyword(s):  
Laser Plasma ◽  
Sample Entropy ◽  
Chaotic Attractors ◽  
Contour Plot ◽  
Coexisting Attractors ◽  
Plasma System ◽  
Plasma Interaction ◽  
Laser Plasma Interaction ◽  
Interaction System ◽  
Largest Lyapunov Exponents

In this paper, a 3D laser plasma interaction system is presented, analysed, and implemented. The system has two unstable equilibria, and two types of coexisting attractors in which the coexistence of two periodic orbits and the coexistence of two chaotic attractors can be clearly observed. The multistability behaviours are determined by the bifurcation diagrams, largest Lyapunov exponents, and phase spaces. Moreover, the complexity performance of the laser plasma interaction system is investigated by the contour plot of the Sample Entropy.

scholarly journals Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 678 ◽  
Author(s):  
Yixuan Song ◽  
Fang Yuan ◽  
Yuxia Li
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Random Sequence ◽  
Mathematical Expression ◽  
Digital Signal ◽  
Approximate Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Key Space ◽  
Sequence Generator

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

A Novel Memcapacitor and Its Application in a Chaotic Circuit

2021 ◽  
Author(s):  
Mei Guo ◽  
Ran Yang ◽  
Meng Zhang ◽  
Renyuan Liu ◽  
Yongliang Zhu ◽  
...  
Keyword(s):  
Steady State ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Burst Period ◽  
The Stability ◽  
Fifth Order ◽  
Stable Points

Abstract In this paper, a novel memcapacitor is designed by SBT memristor and two capacitors. A fifth-order memcapacitor and memristor chaotic circuit is proposed. The stability of the equilibrium point of the system is analyzed theoretically. Lyapunov exponents spectra, bifurcation diagrams, poincaré maps and phase diagrams are used to analyze the dynamic behaviors of the system. The results show that under different initial values and parameters, the system produces rich dynamic behaviors such as stable points, limit cycles, chaos, and so on. Specially, coexisting attractors, transient chaos, and steady-state chaos accompanied by burst period phenomenon are also produced in the system. The proposed memcapacitor-based circuit expands the research methods of memcapacitor for application in chaoticcircuits.

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