Fractional-order Hyperchaotic System Research Articles

A New Fractional-Order Hyperchaotic System and Its Adaptive Tracking Control

We construct for the first time a fractional-order hyperchaotic system via the original integer-order system. The dynamical behavior of this fractional-order hyperchaotic system is investigated in detail using first approximation method and Lyapunov exponents. Next, an adaptive control strategy for the univariate controlled hyperchaotic system has been proposed. Also, the tracking performance is fully taken into account in numerous applications, for instance, tracking sinusoidal periodic signal, self-synchronization, and generalized synchronization of heterogeneous structure. Simulation results illustrate the validity and performability of the proposed adaptive tracking control scheme.

A novel audio encryption approach via finite-time synchronization of fractional order hyperchaotic system

Synchronization of 4-D nonlinear fractional order hyperchaotic system with external disturbance is important models for encryption and decryption technique. In this paper, the fractional order 0 < α ≤ 1 is consider to establish finite-time control for synchronization of sender and receiver system. An audio encryption and decryption algorithms are investigated based on converting an audio data samples into image data. A random mask generated from chaotic mask is used to encrypt and decrypt the audio signals. The path of error system of fractional order hyperchaotic system is shown to be highly better than the classical one. Further, high level security of the proposed work is entrusted or assured by analyzing various metrics including MSE, PSNR, SSIM, NPCR and SNR along with numerical simulations.

Delayed outputs fractional-order hyperchaotic systems synchronization for images encryption

Communication networks, play a major role in keeping us connected and sharing the details of our lives with each other. The main driver of multimedia data transmission is to enhance security protection of this multimedia data (speech, image and video). In this paper we addresses the synchronization problem of the masterslave type via a static error feedback. Sufficient conditions expressed by means of linear matrix inequalities (LMI) for the synchronization of fractional-order hyperchaotic systems with a known time delay between them is presented. The delay-dependent criterion is given based upon a Lyapunov function. We take the fractional-order hyperchaotic Liu system as an illustrative example to demonstrate the effectiveness of the proposed synchronization scheme. Moreover, as an application an images cryptosystem is presented. We considered two scenarios corresponding to the transmission channel, under occlusion attack and under noisse addition respectively. Results for the studied scenarios are presented and compared. The extensive simulation results prove that proposed cryptosystem has clear advantage over other proposed in the litterature.

A fractional-order CNN hyperchaotic system for image encryption algorithm

This paper proposes a fractional-order cellular neural network (CNN) chaotic system for image encryption algorithm to explore the application of fractional-order CNN hyperchaotic system in chaotic secure communication. Firstly, a fractional-order CNN hyperchaotic system is defined based on CNN hyperchaotic system. The numerical solutions of the fractional-order CNN hyperchaotic system are calculated by Adomian decomposition algorithm. The dynamic characteristics of the of the fractional-order CNN hyperchaotic system are analyzed. Then to verify the image encryption application of the fractional-order CNN hyperchaotic system, we designed an image encryption scheme through fractional-order CNN hyperchaotic sequence, the principle of symmetry of main diagonal of matrix and XOR operation. Finally, the results illustrate that the fractional-order CNN hyperchaotic sequence has good randomness, which show that the fractional-order CNN hyperchaotic system more suitable for chaotic secure communication applications. The security performances of the algorithm show that the designed algorithm can effectively encrypt and decrypt image, and has better security performance.

A new approach for security of wireless sensor networks based on anti-synchronization of the fractional-order hyper-chaotic system

Chaotic systems have wide applications in secure communication engineering and cryptography. In this paper, improved nonlinear predictive control with whale algorithm for anti-synchronization of a fractional-order economic hyper-chaotic system is used for increasing the security of wireless sensor networks and preventing intrusion. By chaotic masking method and the T-S fuzzy model, the message signal is encoded at the wireless sensor side and it is placed along the transmitter route. In the central station, the message signal is decoded using the T-S fuzzy model and the predictive control by anti-synchronizing the fractional-order hyper-chaotic slave system. To reduce the effect of disturbances, a sign function of error is added to the predictive control. Finally, simulation results indicate the proper performance of the proposed nonlinear predictive control for anti-synchronizing the fractional-order hyper-chaotic systems in secure communications.

On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative

In this paper, we consider a class of fractional-order systems described by the Caputo derivative. The behaviors of the dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to obtain the phase portraits. Before that, we will provide the conditions under which the considered fractional-order system’s solution exists and is unique. The fractional-order impact will be analyzed, and the advantages of the fractional-order derivatives in modeling chaotic systems will be discussed. How the parameters of the model influence the considered fractional-order system will be studied using the Lyapunov exponents. The topological changes of the systems and the detection of the chaotic and hyperchaotic behaviors at the assumed initial conditions and the considered fractional-order systems will also be investigated using the Lyapunov exponents. The investigations related to the Lyapunov exponents in the context of the fractional-order derivative will be the main novelty of this paper. The stability analysis of the model’s equilibrium points has been focused in terms of the Matignon criterion.

Synchronization precision analysis of a fractional-order hyperchaos with application to image encryption

This paper proposes an effective image encryption algorithm based on the transformational prospective synchronization of a fractional-order hyperchaotic system. Compared with other chaos-based algorithms, fractional orders and synchronization precision are added as secret keys. It is shown that fractional-order, in comparison with its integer counterpart, has bigger complexity and larger key-space. Numerical simulation test results and security analyses demonstrate good performance of the proposed algorithm by encrypting the color image, gray medical image, and binary image. Furthermore, it is found that the synchronization precision accounted for in the decryption process has a significant effect on the decryption resolution.

Double image compression-encryption algorithm based on fractional order hyper chaotic system and DNA approach

In order to improve the efficiency and security of image compression-encryption algorithms, we propose a double image compression-encryption scheme based on fractional hyper-chaotic system and DNA approach. Firstly, two images are processed by discrete cosine transform. Secondly, the spectrums of the two images are sorted by Z-scan, so that the two images can be compressed and mixed into a new image. Finally, the resulting image is encrypted by using DNA coding. Different from traditional image encryption algorithms, the proposed algorithm provides a variety of DNA coding and operation modes. Chaotic sequences are used to control the coding and operation mode in order to improve the complexity of the encryption process. Fractional order and initial values of fractional order hyper-chaotic system are used as the key of the proposed algorithm, which greatly expands the complexity and the key space of the scheme. In the proposed scheme, by mixing two images and performing a compression-encryption operation on them simultaneously, the proposed algorithm can improve the complexity of encrypted images while providing good confusion. Experimental results and security analysis show that the proposed algorithm can effectively resist multiple attacks.

Robust finite-time sliding mode synchronization of fractional-order hyper-chaotic systems based on adaptive neural network and disturbances observer

In this paper, a novel sliding mode control method based on neural network and disturbances observer is designed to satisfy the synchronization of hyper-chaotic fractional-order systems in finite time. It is completely robust against unknown uncertainties and external disturbances. Compared with existing methods, an adaptive neural network and disturbances observer existing in sliding mode law can lessen the chattering effectively. Numerical simulations are applied to demonstrate the efficiency of the proposed control method.

An image encryption algorithm based on BP neural network and hyperchaotic system

To reduce the bandwidth and storage resources of image information in communication transmission, and improve the secure communication of information. In this paper, an image compression and encryption algorithm based on fractional-order memristive hyperchaotic system and BP neural network is proposed. In this algorithm, the image pixel values are compressed by BP neural network, the chaotic sequences of the fractional-order memristive hyperchaotic system are used to diffuse the pixel values. The experimental simulation results indicate that the proposed algorithm not only can effectively compress and encrypt image, but also have better security features. Therefore, this work provides theoretical guidance and experimental basis for the safe transmission and storage of image information in practical communication.

Initial boosting phenomenon of a fractional-order hyperchaotic system based on dual memristors

In this paper, a fractional-order hyperchaotic system based on dual memristors is represented to analyze the nonlinear dynamic behaviors via replacing two coupled resistors with dual memristors. It is worthy to note that the fractional-order hyperchaotic system has two zero eigenvalues and three nonzero eigenvalues, therefore the equilibrium plane can be separated into diverse areas which indicates the hyperchaotic system is stable or chaotic. The simulation results illustrate that the initial states have a significant impact on the dynamic behaviors, which can be mirrored by the phase portraits, the bifurcation diagrams, the power spectrum and the time-domain waveform. In particular, the memristor initial boosting phenomenon is investigated in the proposed hyperchaotic system, which implies the memristor initial states determine the attractor offset boosting behaviors under various initial controllers. Clearly, it differs from the variable offset boosting behavior totally due to its multi-dimension and nonlinearity. Finally, numerical results under different initial controllers are exhibited to demonstrate the memristor initial boosting phenomenon. Moreover, a hardware circuit based on PSPICE software is fabricated and its experimental simulations is given to verify the dynamic behaviors effectively.

Anticontrol of a Fractional-Order Chaotic System and Its Application in Color Image Encryption

This paper investigates the anticontrol of the fractional-order chaotic system. The necessary condition of the anticontrol of the fractional-order chaotic system is proposed, and based on this necessary condition, a 3D fractional-order chaotic system is driven to two new 4D fractional-order hyperchaotic systems, respectively, without changing the parameters and fractional order. Hyperchaotic properties of these new fractional dynamic systems are confirmed by Lyapunov exponents and bifurcation diagrams. Furthermore, a color image encryption algorithm is designed based on these fractional hyperchaotic systems. The effectiveness of their application in image encryption is verified.

Compound Difference Anti-Synchronization between Hyper-Chaotic Systems of Fractional Order

In this article, the compound difference anti-synchronization between fractional order hyper-chaotic systems have been studied. Numerical simulations have been performed using MATLAB to verify the theoretical results on fractional order Xling, Vanderpol, Rikitake and Rabinovich hyper-chaotic systems.

A new approach in anti-synchronization of a fractional-order hyper-chaotic Duffing system based on new nonlinear predictive control

In this paper, we have carried out a new method for the anti-synchronization of a fractional-order hyperchaotic Duffing system using the nonlinear predictive control. At first, in this method master and slave systems are modeled using Takagi–Sugeno fuzzy model, Then, nonlinear predictive controller based on proposed model, is applied to the system to achieve the aim of the anti-synchronization. In this controller, the feedback coefficients of the error are set using the teaching learning based optimization, so that the cost function, which is including the error and control effort, becomes minimized. The advantage of the proposed method is the robustness of the controller against uncertainty and disturbance. Simulating results showed that, the proposed method has been able to anti-synchronize the master and slave fractional-order hyperchaotic Duffing systems with uncertainty and disturbance in highly accurately manner.

One-to-four-wing hyperchaotic fractional-order system and its circuit realization

PurposeThis 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/approachA 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 C0algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of orderqon the system is also investigated. Finally, the circuit is implemented using physical components.FindingsThe 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 parameterdor the orderq. 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/valueThe 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.

Anti-synchronisation of non-identical fractional order hyperchaotic systems

This paper deals with the anti-synchronisation of fractional order hyperchaotic systems. In particular, we employ the active control method to achieve complete anti-synchronisation between fractional order Lorenz and Chen hyperchaotic systems. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Numerical simulations demonstrate the feasibility of the proposed algorithm.

Anti-synchronisation of non-identical fractional order hyperchaotic systems

This paper deals with the anti-synchronisation of fractional order hyperchaotic systems. In particular, we employ the active control method to achieve complete anti-synchronisation between fractional order Lorenz and Chen hyperchaotic systems. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Numerical simulations demonstrate the feasibility of the proposed algorithm.

Color Image Compression-Encryption Using Fractional-Order Hyperchaotic System and DNA Coding

Recently, many encryption algorithms based on fractional-order chaotic system have been proposed to solve the problem of image encryption. In this paper, we propose a novel color image compression-encryption algorithm based on fractional-order hyperchaotic system and DNA coding. In the data compression stage, the data of R, G, and B channels of the color image are converted to the frequency domain by two-dimensional discrete cosine transform (DCT), and then the amount of encrypted data is reduced by the quantization process. We design a data processing algorithm to ensure that the data after DCT is compatible with DNA coding data format. In the encryption stage, the processes of DNA encoding and decoding, DNA operation, and pixel scrambling are all controlled by the corresponding chaotic sequences, which are generated by the chaotic system. The original image is used to calculate the initial state of the chaotic system, which improves the performance of the algorithm against the chosen-plaintext attack significantly. Experimental results and security analysis illustrate that the proposed algorithm has excellent compression and security performance. It can not only reconstruct the original image well under the condition of low compression ratio, but also provide high security to resist various attacks. Besides, experimental results also indicate that the algorithm proposed can be applied to the fields of color image compression, encryption, and transmission.

Systematic construction of high dimensional fractional-order hyperchaotic systems

Abstract The problem of designing fractional-order hyperchaotic systems (FOHSs) by a consistent and systematic procedure is still an open one at large. The tedious hit and trial design procedures adopted in literature to generate hyperchaos pose as a hindrance; especially when the dimension of the system is high. The paper thus presents a solution to the above problem and further discusses the application of FOHSs by putting forward three proposals. First is the design of the simplest possible single state nonlinear feedback controller based on fractional-order stability theorems for creating hyperchaos from a nominal system. The design is organised and even higher dimensional FOHSs can be easily constructed. Secondly, a hybrid synchronisation controller is designed so that the FOHSs obtained using the proposed systematic methodology, are both completely synchronised and antisynchronised simultaneously. Thirdly, a public key cryptographic algorithm is presented using the higher unpredictable nature and complexity of FOHSs to encrypt and decrypt private messages. Two representative examples presented in this work distinctly confirm the effectiveness of the proposed techniques.

Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application

To explore characteristic of a new system with fractional order and complex variables, based on Adomian decomposition method (ADM), its nonlinear dynamical behaviors are discussed by bifurcation diagram, Lyapunov exponent spectrum, spectral entropy (SE) complexity, and DSP implementation. It is found that, for each parameter and order, there exists a large interval to make the system remain a hyper-chaotic state, which illustrates that the hyper-chaotic sequence could be more random to be applied in image encryption. Especially, a novel image encryption algorithm is proposed based on the fractional-order hyper-chaotic complex system and Galois field (GF). The column cyclic shift is used to scrambling part, the GF(17) algorithm is to diffuse pixel value. The security performances of algorithm are also analyzed. Finally, experiment results indicate that the proposed algorithm not only can effectively encrypt image, but also has better security features.