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1 – 10 of 13Yanjun 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 behaviors of…
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.
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This paper aims to propose a new neural-based enhanced extreme learning machine (EELM) algorithm, used as an online adaptive estimation model, regarding undetermined system…
Abstract
Purpose
This paper aims to propose a new neural-based enhanced extreme learning machine (EELM) algorithm, used as an online adaptive estimation model, regarding undetermined system dynamics and containing internal/external perturbations.
Design/methodology/approach
The EELM structure bases on the single layer feed-forward neural (SLFN) model in which the hidden weighting coefficients are initiated in random and the weighting outputs of the SLFN are online modified using an online adaptive rule implemented from Lyapunov stability concept.
Findings
Four different benchmark uncertain chaotic system tests have been satisfactorily investigated for demonstrating the superiority of proposed EELM technique.
Originality/value
Authors confirm that this manuscript is original.
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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 aims of…
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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Muhammad Haris, Muhammad Shafiq, Adyda Ibrahim and Masnita Misiran
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.
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
This work is originally written by the author.
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Hamed Tirandaz and Ali Karami-Mollaee
The purpose of this paper is to propose a novel and secure image transmission based on the unpredictable behavior of the chaotic systems.
Abstract
Purpose
The purpose of this paper is to propose a novel and secure image transmission based on the unpredictable behavior of the chaotic systems.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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F.J. Farsana, V.R. Devi and K. Gopakumar
This paper introduces an audio encryption algorithm based on permutation of audio samples using discrete modified Henon map followed by substitution operation with keystream…
Abstract
This paper introduces an audio encryption algorithm based on permutation of audio samples using discrete modified Henon map followed by substitution operation with keystream generated from the modified Lorenz-Hyperchaotic system. In this work, the audio file is initially compressed by Fast Walsh Hadamard Transform (FWHT) for removing the residual intelligibility in the transform domain. The resulting file is then encrypted in two phases. In the first phase permutation operation is carried out using modified discrete Henon map to weaken the correlation between adjacent samples. In the second phase it utilizes modified-Lorenz hyperchaotic system for substitution operation to fill the silent periods within the speech conversation. Dynamic keystream generation mechanism is also introduced to enhance the correlation between plaintext and encrypted text. Various quality metrics analysis such as correlation, signal to noise ratio (SNR), differential attacks, spectral entropy, histogram analysis, keyspace and key sensitivity are carried out to evaluate the quality of the proposed algorithm. The simulation results and numerical analyses demonstrate that the proposed algorithm has excellent security performance and robust against various cryptographic attacks.
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Hanène Medhaffar, Moez Feki and Nabil Derbel
The purpose of this paper is to investigate the stabilization of unstable periodic orbits of Chua’s system using adaptive fuzzy sliding mode controllers with moving surface.
Abstract
Purpose
The purpose of this paper is to investigate the stabilization of unstable periodic orbits of Chua’s system using adaptive fuzzy sliding mode controllers with moving surface.
Design/methodology/approach
For this aim, the sliding mode controller and fuzzy systems are combined to achieve the stabilization. Then, the authors propose a moving sliding surface to improve robustness against uncertainties during the reaching phase, parameter variations and extraneous disturbances.
Findings
Afterward, the authors design a sliding observer to estimate the unmeasurable states which are used in the previously designed controller.
Originality/value
Numerical results are provided to show the effectiveness and robustness of the proposed method.
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Quanli Deng, Chunhua Wang, Yazheng Wu and Hairong Lin
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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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.
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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 chemical…
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.
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