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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: 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: 3 October 2019

Lei Zhu, Minghai Pan and Xiaohua Qiao

This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework.

Abstract

Purpose

This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework.

Design/methodology/approach

In this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter.

Findings

Compared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor.

Originality/value

The newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.

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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

Keywords

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Article
Publication date: 23 April 2018

Quan Xu, Qinling Zhang, Tao Jiang, Bocheng Bao and Mo Chen

The purpose of this paper is to develop a simple chaotic circuit. The circuit can be fabricated by less discrete electronic components, within which complex dynamical…

Abstract

Purpose

The purpose of this paper is to develop a simple chaotic circuit. The circuit can be fabricated by less discrete electronic components, within which complex dynamical behaviors can be generated.

Design/methodology/approach

A second-order non-autonomous inductor-free chaotic circuit is presented, which is obtained by introducing a sinusoidal voltage stimulus into the classical Wien-bridge oscillator. The proposed circuit only has two dynamic elements, and its nonlinearity is realized by the saturation characteristic of the operational amplifier in the classical Wien-bridge oscillator. After that, its dynamical behaviors are revealed by means of bifurcation diagram, Lyapunov exponent and phase portrait and further confirmed using the 0-1 test method. Moreover, an analog circuit using less discrete electronic components is implemented, and its experimental results are measured to verify the numerical simulations.

Findings

The equilibrium point located in a line segment varies with time evolution, which leads to the occurrence of periodic, quasi-periodic and chaotic behaviors in the proposed circuit.

Originality/value

Unlike the previously published works, the significant values of the proposed circuit with simple topology are inductor-free realization and without extra nonlinearity, which make the circuit can be used as a paradigm for academic teaching and experimental illustraction for chaos.

Details

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

Keywords

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Article
Publication date: 31 December 2020

Kapil Bhardwaj and Mayank Srivastava

This paper aims to develop a mathematical model for four-lobe memristor (FLM) element. The four-lobe memristive behaviour can be used in realization of hyperchaotic…

Abstract

Purpose

This paper aims to develop a mathematical model for four-lobe memristor (FLM) element. The four-lobe memristive behaviour can be used in realization of hyperchaotic oscillators and implementation of multi-bit memories. For verification of the developed mathematical framework, two FLM circuit emulators have been presented using VDCC and IC LM13700, respectively.

Design/methodology/approach

A mathematical model for FLM has been developed in which, the condition for the existence of symmetrical four lobes, instances and coordinates of the end points of lobes has been derived and presented. Using this mathematical framework, a FLM emulator based on VDCC has been developed. To validate the possibility of practical implementation of FLM concept, an IC LM13700-based circuit has also been developed. The workability of VDCC based circuit has been verified by running simulations in PSPICE environment using CMOS VDCC model. Similarly, the behaviour of LM13700 IC-based circuit has been confirmed by SPICE model of LM13700 IC.

Findings

It has been shown mathematically that under certain conditions, third-order flux dependent equation of memductance can be used to generate four lobes on the transient v-i plane. Also, two FLM emulators without using any voltage multiplier circuit/IC have been reported.

Originality/value

From the best knowledge of the authors, there are no such FLM emulators that have been reported in literature so far, which operates at practical operating frequencies.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 40 no. 1
Type: Research Article
ISSN: 0332-1649

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: 4 October 2018

Bocheng Bao, Jiaoyan Luo, Han Bao, Quan Xu, Yihua Hu and Mo Chen

The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the…

Abstract

Purpose

The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors.

Design/methodology/approach

This paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit.

Findings

The system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit.

Originality/value

These memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.

Details

Circuit World, vol. 44 no. 4
Type: Research Article
ISSN: 0305-6120

Keywords

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Article
Publication date: 6 May 2020

Poornima Sridharan and Pugazhendhi Sugumaran C.

An annual substation equipment failure report says 3/7 capacitive voltage transformer (CVT) got damaged because of ferroresonance overvoltage. The conventional mitigation…

Abstract

Purpose

An annual substation equipment failure report says 3/7 capacitive voltage transformer (CVT) got damaged because of ferroresonance overvoltage. The conventional mitigation circuit fails to protect the transformer as the overvoltage may fall in the range between 2 and 4 per unit. It is necessary to develop a device to suppress the overvoltage as well as overcurrent of the CVT. This study aims to propose the suitability of memristor emulator as a mitigation circuit for ferroresonance.

Design/methodology/approach

The literature implies that a nonlinear circuit can protect the transformer against ferroresonance. An attempt is made with a memristor emulator using Operational Amplifier (OPAMP) for the mitigation of ferroresonance in a prototype transformer. The circuit is simulated using PSpice and validated for its ideal characteristics using hardware implementation. The nonlinear memductance is designed which is required to mitigate the ferroresonance. The mitigation performance has been compared with conventional method along with fast Fourier transform (FFT) analysis.

Findings

While the linear resistor recovers the secondary voltage by 74.1%, the memristor emulator does it by 82.05% during ferroresonance. Also, the total harmonic distortion (THD) of ferroresonance signal found to be 22.06% got improved as 2.56% using memristor emulator.

Research limitations/implications

The suitability of memristor emulator as a mitigation circuit for ferroresonance is proposed in this paper. As ferroresonance occurs in instrument transformers which have extra high voltage (EHV) rated primary windings and (110 V/[110 V/1.732]) rated secondary windings, the mitigation device is proposed to be connected as a nonlinear load across the secondary windings of the transformer. This paper discusses the preliminary work of ferroresonance mitigation in a prototype transformer. The mitigation circuit may have memristor or meminductor for ferroresonance mitigation when they are commercially available in future.

Practical implications

The electronic component-based memristor emulator may not work at 110 V practically as they may be rated at low power. Hence, chemical component-based memristor emulator was developed to do the same. The authors like to clarify that the memristor will be a solution for ferroresonance in future not the memristor emulator circuit.

Social implications

With the real form of memristor, the transistor world will be replaced by it and may have a revolution in the field of electronics, VLSI, etc. This contribution attempts to project the use of memristor in a smaller scale in high-voltage engineering.

Originality/value

The electronic component-based memristor emulator is proposed as a mitigation circuit for ferroresonance. The hypothesis has been verified successfully in a prototype transformer. Testing circuit of memristor emulator involves transformer, practically. The mitigation performance has been compared with conventional method technically and justified with FFT analysis.

Details

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

Keywords

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Article
Publication date: 5 March 2021

Kapil Bhardwaj and Mayank Srivastava

The purpose of the paper is to report an emulation configuration of a three pinch-off memristor (TPM), whose transient characteristics consist three cross-over points on…

Abstract

Purpose

The purpose of the paper is to report an emulation configuration of a three pinch-off memristor (TPM), whose transient characteristics consist three cross-over points on the voltage-current plane, which is dissimilar to a conventional memristor. These characteristics can be very useful in memristor-based multi-bit memory devices and hyperchaotic oscillators.

Design/methodology/approach

The work describes the Mathematical framework for TPM and a circuit emulator based on the derived conditions. The configuration is based on five operational transconductance amplifier (OTAs) and four grounded passive elements. After which, we have verified its operation using personal simulation program with integrated circuit emphasis simulation environment. Finally, the implementation of OTA-based TPM using commercial integrated circuit (IC) LM13700 has also been presented.

Findings

It has been shown that a flux-dependent memductance expression of cubic order can show three intersections on the VI contour under certain parameter related constraints. Moreover, the OTA-based emulator reported in the work is very compact in nature because of the no use of external multiplier IC/circuitry, which has been popular in previous emulators.

Originality/value

For the first time, a multiple cross-over memristor emulator has been reported which can operate under practical operating conditions such as at practical operating frequencies and sinusoidal excitation.

Details

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

Keywords

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