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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The purpose of this paper is to develop an field programmable gate array (FPGA)-based neuron circuit to mimic dynamical behaviors of tabu learning neuron model.

Numerical investigations for the tabu learning neuron model show the coexisting behaviors of bi-stability. To reproduce the numerical results by hardware experiments, a digitally FPGA-based neuron circuit is constructed by pure floating-point operations to guarantee high computational accuracy. Based on the common floating-point operators provided by Xilinx Vivado software, the specific functions used in the neuron model are designed in hardware description language programs. Thus, by using the fourth-order Runge-Kutta algorithm and loading the specific functions orderly, the tabu learning neuron model is implemented on the Xilinx FPGA board.

With the variation of the activation gradient, the initial-related coexisting attractors with bi-stability are found in the tabu learning neuron model, which are experimentally demonstrated by a digitally FPGA-based neuron circuit.

Without any piecewise linear approximations, a digitally FPGA-based neuron circuit is implemented using pure floating-point operations, from which the initial conditions-related coexisting behaviors are experimentally demonstrated in the tabu learning neuron model.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Many practical applications of neural networks require the identification of non‐linear deterministic systems or chaotic systems. In these cases the use of a network architecture known as locally recurrent neural network (LRNN) is often preferable in place of standard feedforward multi‐layer perceptron (MLP) networks, or of globally recurrent neural network. In this paper locally recurrent networks are used to simulate the behaviour of the Chua’s circuit that can be considered a paradigm for studying chaos. It is shown that such networks are able to identify the underlying link among the state variables of the Chua’s circuit. Moreover, they are able to behave like an autonomous Chua’s double scroll, showing a chaotic behaviour of the state variables obtainable through a suitable circuit elements choice.