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Article
Publication date: 7 August 2017

Li Xiong, Zhenlai Liu and Xinguo Zhang

Lack of optimization and improvement on experimental circuits precludes comprehensive statements. It is a deficiency of the existing chaotic circuit technology. One of the…

Abstract

Purpose

Lack of optimization and improvement on experimental circuits precludes comprehensive statements. It is a deficiency of the existing chaotic circuit technology. One of the aims of this paper is to solve the above mentioned problems. Another purpose of this paper is to construct a 10 + 4-type chaotic secure communication circuit based on the proposed third-order 4 + 2-type circuit which can output chaotic phase portraits with high accuracy and high stability.

Design/methodology/approach

In Section 2 of this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new third-order Lorenz-like chaotic system is proposed based on the 4 + 2 circuit. Then some simulations are presented to verify that the proposed system is chaotic by using Multisim software. In Section 3, a fourth-order chaotic circuit is proposed on the basis of the third-order 4 + 2 chaotic circuit. In Section 4, the circuit design method of this paper is applied to chaotic synchronization and secure communication. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. In Section 5, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented in an analog electronic circuit. The analog circuit implementation results match the Multisim results.

Findings

The simulation results show that the proposed fourth-order chaotic circuit can output six phase portraits, and it can output a stable fourth-order double-vortex chaotic signal. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. The scheme has the advantages of clear thinking, efficient and high practicability. The experimental results show that the precision is improved by 2-3 orders of magnitude. Signal-to-noise ratio meets the requirements of engineering design. It provides certain theoretical and technical bases for the realization of a large-scale integrated circuit with a memristor. The proposed circuit design method can also be used in other chaotic systems.

Originality/value

In this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new chaotic system is proposed on the basis of the 4 + 2 chaotic circuit for the first time. Some simulations are presented to verify its chaotic characteristics by Multisim. Then the novel third-order 4 + 2 chaotic circuit is applied to construct a fourth-order chaotic circuit. Simulation results verify the existence of the new fourth-order chaotic system. Moreover, a new 10 + 4-type chaotic secure communication circuit is proposed based on chaotic synchronization of the novel third-order 4 + 2 circuit. To illustrate the effectiveness of the proposed scheme, the intensity limit and stability of the transmitted signal, the characteristic of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. Finally, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented through an analog electronic circuit, which are characterized by their high accuracy and good robustness. The analog circuit implementation results match the Multisim results.

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Article
Publication date: 4 January 2021

Meiting Liu, Wenxin Yu, Junnian Wang, Yu Chen and Yuyan Bian

In this paper, a nine-dimensional chaotic system is designed and applied to secure communication.

Abstract

Purpose

In this paper, a nine-dimensional chaotic system is designed and applied to secure communication.

Design/methodology/approach

Firstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences.

Findings

The proposed nine-dimensional system has a large key space and more complex dynamic characteristics

Originality/value

The results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.

Details

Circuit World, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0305-6120

Keywords

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Article
Publication date: 24 July 2019

Zehra Gulru Cam Taskiran, Murat Taşkıran, Mehmet Kıllıoğlu, Nihan Kahraman and Herman Sedef

In this work, a true random number generator is designed by sampling the double-scroll analog continuous-time chaotic circuit signals.

Abstract

Purpose

In this work, a true random number generator is designed by sampling the double-scroll analog continuous-time chaotic circuit signals.

Methodology

A Chua circuit based on memristance simulator is designed to obtain a non-linear term for a chaotic dynamic system. It is implemented on the board by using commercially available integrated circuits and passive elements. A low precision ADC which is commonly found in the market is used to sample the chaotic signals. The mathematical analysis of the chaotic circuit is verified by experimental results.

Originality

It is aimed to be one of the pioneering studies (including low precision ADC) in the literature on the implementation of memristive chaotic random number generators.

Findings

Two new methods are proposed for post-processing and creating random bit array using XOR operator and J-K flip flop. The bit stream obtained by a full-hardware implementation successfully passed the NIST-800-22 test. In this respect, the availability of the memristance simulator circuit, memristive chaotic double-scroll attractor, proposed random bit algorithm and the randomness of the memristive analog continuous-time chaotic true number generator were also verified.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 4 July 2018

Yanjun Lu, Li Xiong, Yongfang Zhang, Peijin Zhang, Cheng Liu, Sha Li and Jianxiong Kang

This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical…

Abstract

Purpose

This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components.

Design/methodology/approach

The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors.

Findings

Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist.

Originality/value

The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.

Details

Circuit World, vol. 44 no. 3
Type: Research Article
ISSN: 0305-6120

Keywords

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Article
Publication date: 15 November 2019

Li Xiong, Xinguo Zhang and Yan Chen

The ammeter can measure the direct current and low-frequency alternating current through the wires, but it is difficult to measure complex waveforms. The oscilloscope can…

Abstract

Purpose

The ammeter can measure the direct current and low-frequency alternating current through the wires, but it is difficult to measure complex waveforms. The oscilloscope can measure complex waveforms, but it is easy to measure the voltage waveform and difficult to measure the current waveform. Thus, how to measure complex current waveforms with oscilloscope is an important and crucial issue that needs to be solved in practical engineering applications. To solve the above problems, an active short circuit line method is proposed to measure the volt-ampere characteristic curve of chaotic circuits.

Design/methodology/approach

In this paper, an active short circuit line method is proposed to measure the volt-ampere characteristic curve of various chaotic circuits especially for memristive systems. A memristor-based chaotic system is introduced, and the corresponding memristor-based circuit is constructed and implemented by using electronic components.

Findings

The chaotic attractors and volt-ampere characteristic curve of the memristor-based chaotic circuit are successfully analyzed and verified by oscilloscope measurement with the proposed active short circuit line method. Accordingly, the hardware circuit experiments are carried out to validate the effectiveness and feasibility of the active short circuit line method for these chaotic circuits. A good agreement is shown between the numerical simulations and the experimental results.

Originality/value

The primary contributions of this paper are as follows: an active short circuit line method for measuring the volt-ampere characteristic curve of chaotic circuits is proposed for the first time. A memristor-based chaotic system is also constructed by using memristor as nonlinear term. Then, the active short circuit line method is applied to measure the volt-ampere characteristic curve of the corresponding memristor-based chaotic circuit.

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Article
Publication date: 17 June 2019

Li Xiong, Wanjun Yin and Xinguo Zhang

This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new…

Abstract

Purpose

This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new chemical oscillating system is discussed, and it is found that the state selection is dependent on initial values. Then, the stabilization problem of the chemical oscillating attractors is investigated analytically and numerically. Subsequently, the novel electronic circuit of the proposed chemical oscillating chaotic system are constructed, and the influences of the changes of circuit parameters on chemical oscillating chaotic attractors are investigated.

Design/methodology/approach

The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. Moreover, the active control and adaptive control methods are presented to make the chemical oscillating chaotic systems asymptotically stable at the origin based on the Lyapunov stability theory. The influences on chemical oscillating chaotic attractors are also verified by changing the circuit parameters.

Findings

It is found that the active control method is easier to be realized by using physical components because of its less control signal and lower cost. It is also confirmed that the adaptive control method enjoys strong anti-interference ability because of its large number of selected controllers. What can be seen from the simulation results is that the chaotic circuits are extremely dependent on circuit parameters selection. Comparisons between MATLAB simulations and Multisim simulation results show that they are consistent with each other and demonstrate that changing attractors of the chemical oscillating chaotic system exist. It is conformed that circuit parameters selection can be effective to control and realize chaotic circuits.

Originality/value

The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. The characteristic of the chemical oscillating attractor is that the basin of attraction of the three-dimensional attractor is located in the first quadrant of the eight quadrants of the three-dimensional space, and the ranges of the three variables are positive. This is because the concentrations of the three chemical substances are all positive.

Details

Circuit World, vol. 45 no. 2
Type: Research Article
ISSN: 0305-6120

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Article
Publication date: 1 October 2006

Mustafa Türk and Fikret Ata

The purpose of this paper is to present a simulation and realization of the different types of chaotic attractors using the generalized Chua's circuit equations.

Abstract

Purpose

The purpose of this paper is to present a simulation and realization of the different types of chaotic attractors using the generalized Chua's circuit equations.

Design/methodology/approach

This paper presents n+n‐scroll and 2D n‐scroll chaotic attractors by introducing multiple breakpoints to the nonlinearity. Two piece‐wise linear elements controlled with x‐ and y‐state space variables are used. Chaotic scrolls are originated through both x‐ and y‐axes. The current feedback operational amplifiers are preferred in the experimental circuits because of their wide bandwidth.

Findings

It is possible to increase the number of the scrolls in two directions by varying the number of breakpoints in the piece‐wise linear characteristics or changing the location of equilibrium points of the system on 2D‐plane. Theoretically developed behaviors are also experimentally tested.

Originality/value

The excellent adaptation is observed between theoretical and experimental results. This paper also provides useful information about how to build the multiple breakpoints nonlinear elements using the simulation results.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 28 January 2020

Xiang Li, Zhijun Li and Zihao Wen

This paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems…

Abstract

Purpose

This paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems with variable-wing attractors, although some chaotic systems can generate one-to-four-wing attractors, none of them are hyperchaotic attractors, which is incomplete for the dynamic characteristics of chaotic systems.

Design/methodology/approach

A novel 4D fractional-order hyperchaotic system is proposed based on the classical three-dimensional Lü system. The complex and abundant dynamic behaviors of the fractional-order system are analyzed by phase diagrams, bifurcation diagrams and the corresponding Lyapunov exponents. In addition, SE and C0 algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of order q on the system is also investigated. Finally, the circuit is implemented using physical components.

Findings

The most particular interest is that the system can generate one-to-four-wing hyperchaotic attractors with only one parameter variation. Then, the hardware circuit experimental results tally with the numerical simulations, which proves the validity and feasibility of the fractional-order hyperchaotic system. Besides, under different initial conditions, coexisting attractors can be obtained by changing the parameter d or the order q. Then, the complexity analysis of the system shows that the fractional-order chaotic system has higher complexity than the corresponding integer-order chaotic system.

Originality/value

The circuit structure of the fractional-order hyperchaotic system is simple and easy to implement, and one-to-four-wing hyperchaotic attractors can be observed in the circuit. To the best of the knowledge, this unique phenomenon has not been reported in any literature. It is of great reference value to analysis and circuit realization of fractional-order chaotic systems.

Details

Circuit World, vol. 46 no. 2
Type: Research Article
ISSN: 0305-6120

Keywords

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Article
Publication date: 18 May 2021

Selcuk Emiroglu, Akif Akgül, Yusuf Adıyaman, Talha Enes Gümüş, Yılmaz Uyaroglu and Mehmet Ali Yalçın

The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic

Abstract

Purpose

The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented.

Design/methodology/approach

A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions.

Findings

The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison.

Originality/value

The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

Details

Circuit World, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0305-6120

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Article
Publication date: 11 May 2020

Mengjie Hua, Shuo Yang, Quan Xu, Mo Chen, Huagan Wu and Bocheng Bao

The purpose of this paper is to develop two types of simple jerk circuits and to carry out their dynamical analyses using a unified mathematical model.

Abstract

Purpose

The purpose of this paper is to develop two types of simple jerk circuits and to carry out their dynamical analyses using a unified mathematical model.

Design/methodology/approach

Two types of simple jerk circuits only involve a nonlinear resistive feedback channel composited by a nonlinear device and an inverter. The nonlinear device is implemented through parallelly connecting two diode-switch-based series branches. According to the classifications of switch states and circuit types, a unified mathematical model is established for these two types of simple jerk circuits, and the origin symmetry and scale proportionality along with the origin equilibrium stability are thereby discussed. The coexisting bifurcation behaviors in the two types of simple jerk systems are revealed by bifurcation plots, and the origin symmetry and scale proportionality are effectively demonstrated by phase plots and attraction basins. Moreover, hardware experimental measurements are performed, from which the captured results well validate the numerical simulations.

Findings

Two types of simple jerk circuits are unified through parallelly connecting two diode-switch-based series branches and a unified mathematical model with six kinds of nonlinearities is established. Especially, the origin symmetry and scale proportionality for the two types of simple jerk systems are discussed quantitatively. These jerk circuits are all simple and inexpensive, easy to be physically implemented, which are helpful to explore chaos-based engineering applications.

Originality/value

Unlike previous works, the significant values are that through unifying these two types of simple jerk systems, a unified mathematical model with six kinds of nonlinearities is established, upon which symmetrically scaled coexisting behaviors are numerically disclosed and experimentally demonstrated.

Details

Circuit World, vol. 47 no. 1
Type: Research Article
ISSN: 0305-6120

Keywords

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