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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.

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

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.

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

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.

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.

With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).

First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.

The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.

It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.

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.

The purpose of this paper is to propose a novel and secure image transmission based on the unpredictable behavior of the chaotic systems.

The proposed approach includes two main contributions: synchronization scheme and transmission scheme. The synchronization scheme benefits the advantage of the fractional-order active synchronization method. A new control law is derived to asymptotically synchronize the underlined fractional-order Bloch chaotic system. The validity of the proposed synchronization scheme is proved by the Lyapunov stability theorem. Then, a novel image transmission scheme is designed to transfer image data via chaotic signals, which modulates the encrypted data in the sender signals and demodulates it at the receiver side.

Numerical simulations are provided to show the validity and effectiveness of the proposed image transmission system. Furthermore, the performance of the image transmission system is evaluated using some illustrative examples and their corresponding statistical tests. The results demonstrate the effectiveness of the proposed method in comparison with other proposed methods in this subject.

A new chaos-based image transmission system is developed based on the synchronization of Bloch chaotic system. The introduced transmission system is interesting and could be applicable to any kind of secure image/video transmission.

The purpose of this paper is to find a practical active sliding mode control approach for synchronization of two uncertain chaotic systems.

Sliding mode control approach is known to be an efficient alternative way to implement synchronization for uncertain chaotic systems. However, design of traditional sliding mode controller usually needs complex state transformation. Owing to a novel idea of virtual state feedback, a control strategy for synchronization of uncertain chaotic systems is presented, which does not need any complex state transformation. Furthermore, based on Lyapunov stability theory, a sufficient condition is drawn for the robust stability of the error dynamics of synchronization for uncertain chaotic systems.

A novel active sliding mode control approach is proposed to achieve the synchronization of two uncertain chaotic systems.

The main limitation is that uncertainties must meet matched conditions.

The paper presents a useful control approach for synchronization of two uncertain chaotic systems.

The proposed sliding mode control approach based on novel virtual state feedback does not need any complex state transformation, unlike the traditional sliding mode control.

The purpose of this paper is to construct a multiwing chaotic system that has hidden attractors with multiple stable equilibrium points. Because the multiwing hidden attractors chaotic systems are safer and have more dynamic behaviors, it is necessary to construct such a system to meet the needs of developing engineering.

By introducing a multilevel pulse function into a three-dimensional chaotic system with two stable node–foci equilibrium points, a hidden multiwing attractor with multiple stable equilibrium points can be generated. The switching behavior of a hidden four-wing attractor is studied by phase portraits and time series. The dynamical properties of the multiwing attractor are analyzed via the Poincaré map, Lyapunov exponent spectrum and bifurcation diagram. Furthermore, the hardware experiment of the proposed four-wing hidden attractors was carried out.

Not only unstable equilibrium points can produce multiwing attractors but stable node–foci equilibrium points can also produce multiwing attractors. And this system can obtain 2N + 2-wing attractors as the stage pulse of the multilevel pulse function is N. Moreover, the hardware experiment matches the simulation results well.

This paper constructs a new multiwing chaotic system by enlarging the number of stable node–foci equilibrium points. In addition, it is a nonautonomous system that is more suitable for practical projects. And the hardware experiment is also given in this article which has not been seen before. So, this paper promotes the development of hidden multiwing chaotic attractors in nonautonomous systems and makes sense for applications.

The purpose of this paper is to examine the structural and computational potentials of a powerful class of neural networks (NNs), called multiple-valued logic neural networks (MVLNN), for predicting the behavior of phenomenological systems with highly nonlinear dynamics. MVLNNs are constructed based on the integration of a number of neurons working based on the principle of multiple-valued logics. MVLNNs possess some particular features, namely complex-valued weights, input, and outputs coded by kth roots of unity, and a continuous activation as a mean for transferring numbers from complex spaces to trigonometric spaces, which distinguish them from most of the existing NNs.

The presented study can be categorized into three sections. At the first part, the authors attempt at providing the mathematical formulations required for the implementation of ARX-based MVLNN (AMVLNN). In this context, it is indicated that how the concept of ARX can be used to revise the structure of MVLNN for online applications. Besides, the stepwise formulation for the simulation of Chua’s oscillatory map and multiple-valued logic-based BP are given. Through an analysis, some interesting characteristics of the Chua’s map, including a number of possible attractors of the state and sequences generated as a function of time, are given.

Based on a throughout simulation as well as a comprehensive numerical comparative study, some important features of AMVLNN are demonstrated. The simulation results indicate that AMVLNN can be employed as a tool for the online identification of highly nonlinear dynamic systems. Furthermore, the results show the compatibility of the Chua’s oscillatory system with BP for an effective tuning of the synaptic weights. The results also unveil the potentials of AMVLNN as a fast, robust, and efficient control-oriented model at the heart of NMPC control schemes.

This study presents two innovative propositions. First, the structure of MVLNN is modified based on the concept of ARX system identification programming to suit the base structure for coping with chaotic and highly nonlinear systems. Second, the authors share the findings about the learning characteristics of MVLNNs. Through an exhaustive comparative study and considering different rival methodologies, a novel and efficient double-stage learning strategy is proposed which remarkably improves the performance of MVLNNs. Finally, the authors describe the outline of a novel formulation which prepares the proposed AMVLNN for applications in NMPC controllers for dynamic systems.

The purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence.

This article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems.

The designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain.

This work is originally written by the author.