Hyperchaotic System Research Articles

Asymmetrical novel hyperchaotic system with two exponential functions and an application to image encryption

Abstract In this article, asymmetrical novel system with two exponential functions, which can show hyperchaotic behavior, has been proposed. Although new system possesses only one unstable equilibrium. The dynamical behaviors of such system are discovered by computing the Lyapunov exponents and bifurcation diagram. Furthermore, the synchronization of the proposed system are also presented by an adaptive synchronization approach of two identical hyperchaotic systems. An application to image encryption has been obtained.

Analysis of New 4D Hyperchaotic Systems MACM and Implementation Using Runge-kutta

In general, hyperchaotic system is defined as a chaotic system with more than one positive Lyapunov exponent, this implies that its chaotic dynamics extend in several different directions simultaneously. The discovery of reliable and effective methods for solving hyperchaotic systems is carried out extensively. The aim of this research is to implement nonlinear hyperchaotic using runge-kutta. The NHS system is built by inspecting, modifying and adding one state to the MACM chaotic system. In this study, we use the same initial conditions x_0=y_0=z_0=w_0=1 and the parameters a = 2,b = 2,c = 0.5, and d = 14.5. At first we experiments modified approaches, namely Classic Runge-Kutta Method 3 Order, Runge-Kutta Method Based On Arithmetic Mean, Metode Runge-Kutta Method Based On Geometric Mean, Modified Runge-Kutta Geometric Mean Based Method-1, RKLCM Approaches Instead of RKGM using MAPLE software as a calculation tool. In this work, we observe that the Runge-Kutta Method Based on Arithmetic Mean has the smallest error value with an average variable x of 0.000606953, variable y of 0.009280181, variable z of 0.000378639 and variable w of 0.60781585. Then also in RKLCM Approaches Instead of RKGM it has the largest error value with an average variable x of 0.483789793, variable y of 0.620803849, variable z of 0.92097139, and variable w of 0.596137549.

A hyperchaotic memristive system with extreme multistability and conservativeness

A hyperchaotic memristive system with extreme multistability and conservativeness

Predefined-time sliding mode control for synchronization of uncertain hyperchaotic system and application

The main goal of this paper is to investigate the predefined-time sliding mode control and synchronization of uncertain hyperchaotic systems and its application in secure communication. Firstly, a novel predefined-time sliding surface is designed. Then a predefined-time sliding mode controller is proposed for uncertain hyperchaotic systems, which can guarantee synchronization of the master-slave system within a predefined time in the presence of parameter uncertain and external disturbance. Specially, the settling time, as a part of control parameters, can be predefined as needed independent of initial conditions. Furthermore, the validity of the proposed approach is proved by Lyapunov stability theory. Finally, comparative tests and image encryption application are given to show advantages of the proposed method.

Comparative analysis and FPGA realization of different control synchronization approaches for chaos-based secured communication systems.

Synchronization of the chaotic systems has attracted much attention in recent years due to its vital applications in secured communication systems. In this paper, an implementation and comparative analysis of two different control approaches for synchronization between two identical four-dimensional hyperchaotic systems is presented. The two control approaches are the Adaptive nonlinear controller and the linear optimal quadratic regulator LQR. To demonstrate the effectiveness of each controller, the numerical simulation is presented using Matlab/Simulink and the control law is derived. The performance of the proposed controllers is compared based on four factors; response time, squared error integration, energy applied from the controller, and cost function. To measure the robustness of the control approaches, the performance factors are compared when there is a change in system parameters and a variation in the initial conditions. Then the proposed synchronization methods are implemented on the FPGA platform to demonstrate the utilized resources on Field Programmable Gate Array (FPGA) hardware platform and the operation speed. Finally, to generalize the results of the comparison, the study is implemented for the synchronization of another secured communication system consisting of two identical three-dimensional chaotic. The experimental results show that the LQR method is more effective than the Adaptive controller based on the performance factors we propose. Moreover, the LQR is much simpler to implement on hardware and requires fewer resources on the FPGA.

Optimal algorithm for color medical encryption and compression images based on DNA coding and a hyperchaotic system in the moments

Currently, visual data security plays a significant role in various fields, especially in medical imaging. Addressing the challenges associated with limited key space and vulnerability to different types of attacks within current encryption schemes, this work proposes an optimal compression-encryption scheme for large medical images that incorporates elements of Archimedes' optimization algorithm, discrete orthogonal Hahn moments, chaotic systems, and DNA coding. The primary aim of this study is to develop an optimal and exceptionally resilient compression-encryption scheme capable of countering various attack types effectively. This approach is structured into three principal phases: a compression phase harnessing the efficiencies of Hahn's discrete orthogonal moments (HMs) in signal and image representation, coupled with the Archimedes optimization algorithm (AO) to ensure optimal tuning of polynomial parameters (a, b) for superior image reconstruction quality. The encryption phase is performed on the compressed image, using hyperchaotic memristive 4-D (HCM-4D), adapted logistics map (ALM) and DNA coding. Initially, the adapted logistics map is responsible for generating random sequences linked to the compressed image. Subsequently, chaotic sequences originating from the hyperchaotic 4-D memristive system govern both random sequences and DNA processes. The optimization phase, facilitated by the AO algorithm, focuses on minimizing the value of the objective function (correlation) on the compressed and encrypted images. Ultimately, the image with the lowest correlation value is designated as the optimal compressed-encrypted representation.The simulation results clearly illustrate the resilience of the AO algorithm when juxtaposed with other optimization algorithms, especially with respect to convergence speed and computational efficiency. On the other hand, the proposed compression approach demonstrated exceptional efficiency in compressing medical images, offering us the possibility to achieve impressive compression ratio (CR) as well as exceptional quality in decompressed images, evident thanks to high PSNR values. In addition, security analyze demonstrate that the proposed compression-encryption benefits from a larger key space and superior resistance against different types of attacks. Furthermore, our approach was subjected to a comparative analysis alongside various encryption method. These comparisons demonstrate that our encryption algorithm surpasses others in terms of both security and effectiveness.

Investigation of the hyperchaos and control in the fractional order financial system with profit margin

This research study proposes a novel hyperchaotic finance system with profit margin and then utilizes the Adomian Decomposition Method (ADM) to tackle the solution of the associated Caputo-derivative based fractional-order hyperchaotic finance system with profit margin. Numerical simulations and analyses, such as the evaluation of Lyapunov exponents (LE), the creation of bifurcation diagrams (BD), the complexity analysis (CA), and the 0-1 test, are used to get a full picture of the system. The results of our study demonstrate the occurrence of periodic, chaotic, and hyperchaotic dynamics in the system. Furthermore, the overall criteria for the existence and the uniqueness of the exact solutions for Caputo fractional-order models are presented. In addition, we present a control methodology for the fractional-order hyperchaotic financial system utilizing the Laplace transform and linear feedback control. Significantly, our research showcases a noteworthy correlation between the analytical results and numerical simulations, emphasizing the soundness and effectiveness of our methodology.

Color image encryption based on discrete memristor logistic map and DNA encoding

This paper proposes a color image encryption scheme with new features based on two-dimensional discrete memristor logistic map (2D-MLM), Deoxyribonucleic acid (DNA) encoding and multi-wing hyperchaotic systems. Firstly, the discrete memristor map and four-wing hyperchaotic system are used to generate various pseudo-random sequences. Secondly, the original image is processed in blocks, and DNA encoding and operation are performed on the sub-block image using multiple pseudo-random sequences. Finally, combining the pseudo-random sequence to diffuse the sub-block image and DNA decoding, we can get the encrypted image. The scheme generates a one-time key for each image, and uses multiple different sub-keys to increase the key space. The use of diverse pseudo-random sequences for image scrambling effectively avoids the security risks associated with using a single chaotic sequence. The key space of this algorithm reaches 2425, the information entropy of the ciphertext image is 7.9993, the number of pixels change rate (NPCR) and the uniformed average change intensity (UACI) reach 99.6095 % and 33.5089 %, and the inter-pixel correlation is close to zero. The simulation results prove that the proposed algorithm has good security against many potential attacks.

Generalized time-delay reverse synchronization with error feedback coefficients

To enhance the application of discrete chaotic systems in secure communication, we introduce a novel generalized time-delay inverse synchronization method with error feedback coefficient. This paper outlines the derivation of an inverse master-slave time-delay generalized synchronization system using the Lyapunov theory with error feedback coefficient design, which is proposed for the first time. To verify the efficacy of the synchronization method, we constructed a new 4D discrete hyperchaotic system. The dynamic properties of the novel system, such as the phase diagram and Lyapunov exponents, are investigated. Empirical outcomes reveal that generalized discrete time-delay synchronization can be accomplished under certain conditions for the error feedback coefficient. The study utilizes the chaotic masking technique to encrypt and decrypt messages in the secure communication system. The experimental findings reveal that by integrating the synchronization approach with the time-delay context of secure communication, the applicable design of the synchronization procedure is adaptable and trustworthy, catering to the pertinent requirements of engineering, and has the capacity to attain instantaneous chaotic synchronization requisites.

Image encryption algorithm based on DNA network and hyperchaotic system

Image encryption algorithm based on DNA network and hyperchaotic system

6D Hyperchaotic Encryption Model for Ensuring Security to 3D Printed Models and Medical Images

In the 6G era, where ultra-fast and reliable communication is expected to be ubiquitous, encryption shall continue to play a crucial role in ensuring the security and privacy of data. Encryption and decryption of medical images and 3D printed models using 6D hyperchaotic function is proposed in this research work for ensuring security in data transfer. Here we envisage using a six-dimensional hyperchaotic system for encryption purposes which shall offer a high level of security due to its complex and unpredictable dynamics with multiple positive Lyapunov exponents. This system can potentially enhance the encryption process for 3D objects and medical images, ensuring the protection of sensitive data and preventing unauthorized access. A hyperchaotic system is a type of dynamical system characterized by exhibiting more than one positive Lyapunov exponent, which indicates strong sensitivity to initial conditions. These systems have more degrees of freedom and complex and intricate dynamics compared to standard chaotic systems. The security of the encryption scheme depends on the complexity of the hyperchaotic system and the randomness of the secret key. The parameters of a 6D hyperchaotic system shall be used as an encryption key with six dimensions, each with its range of values, and shall provide many possible keys. In this work, we implemented a 6D hyperchaotic system for the encryption of the 3D printed model and medical images. The performance evaluation was done by metrics entropy, correlation, Number of Pixels Change Rate (NPCR), and Unified Averaged Changed Intensity (UACI) which revealed the robustness of the encryption model in ensuring security. Hyperchaotic systems can be efficiently implemented in parallel computing architectures, which allow faster encryption and decryption processes.

An Image Double Encryption Based on Improved GAN and Hyper Chaotic System

An Image Double Encryption Based on Improved GAN and Hyper Chaotic System

Color Image Compression and Encryption Algorithm Based on 2D Compressed Sensing and Hyperchaotic System

Color Image Compression and Encryption Algorithm Based on 2D Compressed Sensing and Hyperchaotic System

New results on finite-time projective synchronization for memristor-based hybrid delayed BAM neural networks with applications to DNA image encryption

<abstract> <p>With the popularization of digital image technology, image information has inevitably developed to involved the disclosure of personal privacy; in this study, a color image encryption algorithm was designed to encrypt and decrypt images by using chaotic sequences of a class of memristor-based hybrid delayed bidirectional associative memory neural networks (MHDBAMNNs) to protect images from illegal acquisition and use. Additionally, the discontinuity problem of the right-hand side of the Filippov system due to the hopping property of the memristor has been treated by using differential inclusion and set-valued mapping theories, and a sufficient criterion for guaranteeing the synchronization of finite-time projections derived based on the drive-response concept, Lyppunov stability theorem, and inequality technique. To improve the security performance, a color image encryption algorithm based on a combination of Chen's hyperchaotic system and a DNA codec operation was adopted, also, the robustness and validity of our proposed approach was demonstrated through image performance analysis. Furthermore, the potential application of the model in secure transmission has been explored.</p> </abstract>

Triple Layer RGB Image Encryption Algorithm Utilizing Three Hyperchaotic Systems and Its FPGA Implementation

Triple Layer RGB Image Encryption Algorithm Utilizing Three Hyperchaotic Systems and Its FPGA Implementation

Controllable multistability of fractional-order memristive Henon map and its application in video encryption

In recent years, the use of discrete memristors to enhance chaotic maps has received increasing attention. The introduction of memristors increases the complexity of chaotic maps, making them suitable for engineering applications based on chaotic systems. In this work, a fractional-order discrete memristor exhibiting local activity and controllable asymptotic stability points is constructed by using multiband nonlinear functions. The locally active property of this memristor is demonstrated by using the power-off plot and DC <i> <b>v</b> </i> -<i> <b>i</b> </i> plot. It is then introduced into the Henon map to construct a fractional-order memristive Henon map that can generate any number of coexisting attractors. Simulation results show that the number of fixed points in the system is controlled by the memristor parameters and related to the number of coexisting attractors, thus achieving controllable homogeneous multistability. The complex dynamical behaviors of this map are analyzed by using phase portraits, bifurcation diagrams, maximum Lyapunov exponent (MLE), and attractor basins. Numerical simulations show that the fractional-order map can generate various periodic orbits, chaotic attractors, and period-doubling bifurcations. The system is then implemented on an ARM digital platform. The experimental results are consistent with the simulation results, confirming the accuracy of the theoretical analysis and its physical feasibility. Finally, a parallel video encryption algorithm is designed by using the chaotic sequence iteratively generated by fraction-order memory Henon mapping, which mainly includes frame pixel scrambling and diffusion. Comprehensive security analyses are conducted, proving the robustness and reliability of the proposed encryption scheme. The results show that the encryption algorithm can effectively protect video information. In the future, we will explore other methods of constructing chaotic or hyperchaotic systems with controllable multistability and study their circuit implementation, synchronization control, and chaos-based engineering applications.

Design and analysis of a novel self-excited 5-D hyperchaotic system with maximum (n-2) positive lyapunov exponents

In this work, analytic and designed a new self -existed 5-D with thirteen terms nine of the term exhibit linearity, while the remaining one demonstrates nonlinearity. It has the highest Lyapunov Exponent with three positive ones to leverage the sequence in data security, encryption, and other related aspects, it’s advantageous to utilize a complex system where the key remains unbreakable It contains fifteen keys sensitive ICs and parameters. The system is a highly intricate dynamical system characterized by two equilibrium points, as demonstrated through examinations such as observation of phase plane trajectories, the investigation into eigenvalue structure, and assessment of dissipative stability. These analyses provide evidence supporting the existence of chaotic and hyperchaotic attractors within the system. The results of the simulations are derived from MATLAB 2021b, and Mathematica 11. A detailed and comprehensive evaluation of the recommended techniques has been carried out, offering insights into their effectiveness and suitability for theoretical computation and numerical simulation.

A new image encryption based on hybrid heterogeneous time-delay chaotic systems

<abstract><p>Chaos theory has been widely utilized in password design, resulting in an encryption algorithm that exhibits strong security and high efficiency. However, rapid advancements in cryptanalysis technology have rendered single system generated sequences susceptible to tracking and simulation, compromising encryption algorithm security. To address this issue, we propose an image encryption algorithm based on hybrid heterogeneous time-delay chaotic systems. Our algorithm utilizes a collection of sequences generated by multiple heterogeneous time-delay chaotic systems, rather than sequences from a single chaotic system. Specifically, three sequences are randomly assigned to image pixel scrambling and diffusion operations. Furthermore, the time-delay chaotic system comprises multiple hyperchaotic systems with positive Lyapunov exponents, exhibiting a more complex dynamic behavior than non-delay chaotic systems. Our encryption algorithm is developed by a plurality of time-delay chaotic systems, thereby increasing the key space, enhancing security, and making the encrypted image more difficult to crack. Simulation experiment results verify that our algorithm exhibits superior encryption efficiency and security compared to other encryption algorithms.</p></abstract>

An <i>n</i>-dimensional discrete hyperchaotic system and its application in audio encryption

Discrete chaotic system, as a pseudo-random signal source, plays a very important role in realizing secure communication. However, many low-dimensional chaotic systems are prone to chaos degradation. Therefore, many scholars have studied the construction of high-dimensional chaotic systems. However, many existing algorithms for constructing high-dimensional chaotic systems have relatively high time complexity and relatively complex structures. To solve this problem, this paper explores an <i>n</i>-dimensional discrete hyperchaotic system with a simple structure. Firstly, the <i>n</i>-dimensional discrete hyperchaotic system is constructed by using sine function and power function and simple operations. Then, it is theoretically analyzed based on Jacobian matrix method that the system can have the positive Lyapunov exponents. Next, the algorithm time complexity, sample entropy, correlation dimension and other indexes are compared with those of the existing methods. The experimental results show that our system has a simple structure, high complexity and good algorithm time complexity. Therewith, a six-dimensional chaotic system is chosen as an example, and the phase diagram, bifurcation diagram, Lyapunov expnonents, complexity and other characteristics of the system are analyzed. The results show that the proposed system has good chaotic characteristics. Moreover, to show the application of the proposed system, we apply it to audio encryption. According to this system, we combine it with the XOR operation and true random numbers to explore a novel method of one-cipher audio encryption. Through experimental simulation, compared with some existing audio encryption algorithms, this algorithm can satisfy various statistical tests and resist various common attacks. It is also validated that the proposed system can be effectively applied to the field of audio encryption.

A 4D Entangled Memristor Hyperchaotic System and Its New Predefined-Time Sliding Mode Synchronization Control

A 4D Entangled Memristor Hyperchaotic System and Its New Predefined-Time Sliding Mode Synchronization Control