Lorenz Chaotic System Research Articles

Fault Diagnosis for Power Cables Based on Convolutional Neural Network With Chaotic System and Discrete Wavelet Transform

In this paper, the discrete wavelet transform (DWT) and a chaotic system were combined with a convolutional neural network (CNN) and applied to the diagnosis of insulation faults in XLPE (cross-linked polyacetylene) power cables. First, four different types of insulation faults in power cables were constructed, including the normal state of the cable, the short outer semi-conducting layer, impurities in the insulation layer, and insulation layer damage, and a high-speed capture card (NI PXI-5105) was adopted to measure the partial discharge (PD) signal, which was then filtered through discrete wavelet transform. Then, based on the Lorenz chaotic system, a dynamic error scatter diagram was established as the feature of each fault state. Finally, the dynamic error scatter diagram was processed by CNN to recognize four different types of faults in the power cable. The test results show that the method proposed in this paper can quickly recognize the fault state of power cables and has excellent performance in terms of recognition accuracy, which reaches 97.5%. Therefore, the proposed method can effectively detect the fault signal changes of power cables and identify the fault state of power cables in real time.

A new hyperchaotic complex system and its synchronization realization

In this paper, we propose a new hyperchaotic complex system and systematically study its basic dynamic characteristics such as dissipation, Lyapunov exponent, attractor, parameter changes, and cross-section. The system is based on the complex Lorenz chaotic system, and the chaotic system has higher dimensionality and more parameters than complex Lorenz system. We provide a general method for constructing complex chaotic systems. We use the state linear feedback method to realize the synchronization control of the chaotic system as the driving system and the response system and simulate all of the systems by Simulink. The chaotic system and its synchronization simulation are simulated by Simulink to verify their hardware feasibility.

Computer Modelling of the Information Properties of Hyper Chaotic Lorenz System and Its Application in Secure Communication System

This paper presents computer modeling, analysis and research of the hyper-chaotic Lorenz system based on programming interface that has been developed in LabView software environment. This study allows for generating and research of the main information properties of hyper-chaotic Lorenz system, focusing on time distribution of the four chaotic coordinates, phase portraits and Lyapunov exponents. The programming interface demonstrates the algorithm of masking and decrypt of the information carrier.

A Low Area FPGA Implementation of Reversible Gate Encryption with Heterogeneous Key Generation

The reversible computation is the process of designing the architecture with reversible logic gates (RLG) and applicable for optical computing, digital signal processing, nanotechnologies and low-power circuits. In this study, integer wavelet transform (IWT) compression technique is applied to the input image to compress the pixel value. The utilization of the IWT is used to improve the quality of the image in terms of peak signal-to-noise ratio (PSNR) and structural similarity index matrix (SSIM). In addition, different types of RLGs are used to perform the encryption and decryption of the images. A random number is generated using the Lorenz chaotic system (LCS) that contains three different stages and each stage is developed using arithmetic blocks. Here, an effective key value is generated from the input image values by connecting the LCS’s output with the heterogeneous key generation (HKG) module. The inverse IWT (IIWT) technique is used to retrieve the original data during execution of decryption operation. Application specific integrated circuit and field-programmable gate array (FPGA) performances are calculated for reversible logic cryptographic design (RLCD) IWT-HKG architecture. The results showed that it has achieved better performance compared to conventional methods. Moreover, security analyses such as avalanche effect, side channel attack and session key agreement are performed for the RLCD-IWT-HKG method. The RLCD-IWT-HKG method has achieved 89 LUTs, 52 flip flops and 31 slices for the Virtex 6 FPGA device. After retrieving the decrypted images, values of PSNR and SSIM are evaluated as 39.90 dB and 0.6874, respectively.

Synthetic Adaptive Fuzzy Disturbance Observer and Sliding-Mode Control for Chaos-Based Secure Communication Systems

This paper aims to present secure communication based on master and slave Lorenz chaotic systems. To apply a form of the linear synchronization control method, the mathematical models of master and slave systems were reformed into Takagi-Sugeno (T-S) fuzzy systems. First, the Lorenz chaotic system was completely changed to the form of the T-S fuzzy model with two sublinear systems and two boundary fuzzy membership functions. Second, a newly adaptive disturbance observer (ADOB) was proposed with a high convergent speed for the synchronization system, which was based on the basic nonlinear disturbance observer. Third, adaptive sliding-mode control (ASMC) has been constructed to synchronize the master and slave systems of a secure communication system. The stability of the proposed control algorithms was shown by solving the Lyapunov condition with the support of Young's inequality. The synchronization of two nonidentical chaotic Lorenz systems was utilized to encrypt and decrypt the data. Transmitted and decrypted signals are used to show that the proposed algorithms are adequate for the secure communication system. To confirm the originality and power of the proposed algorithms, secure communication between two computers was implemented perfectly through an internet router and electronic circuit communication scenarios.

Bearing Fault Diagnosis Based on Chaotic Dynamic Errors in Key Components

Ball bearings are one of the most common components used in rotating machines. They reduce the rotational friction between the shaft and fixed components and maintain the center line of rotation of the shaft. A damaged bearing will cause abnormal vibration and noise, and often results in machine failure and loss of production. In this study the public database on ball bearings, provided by the Vibration Institute of Machinery Failure Prevention Technology (MFPT), was used for data retrieval and analysis, and a diagnosis model was created according to the data sets of the bearing in the database. Three different approaches were used for the extraction of features and a classifier was used to implement a diagnostic system. The aim of this study was a comparison of three approaches. The first was the Short-time Fourier Transform (STFT) where the time-frequency domain image is extracted as the feature used for status identification. The second and third approaches were based on the Chen-Lee Chaotic and the Lorenz Chaotic Systems and chaotic dynamic error maps were used in analysis and feature status identification. Chaotic systems are particularly sensitive to the slightest changes in input signals, and the time domain signals from bearings in different conditions were mapped onto individual images. The feature images extracted by the three different approaches were then used for training and verification in a Convolutional Neural Network (CNN). From the results of the experiments, it can be seen that all three approaches gave high identification rates. The interactive verification identification rate of the Chen-Lee chaotic system with CNN under three statuses reached 98.33%, and it also had the best computational efficiency in the condition without losing any classification accuracy. This will make a substantial contribution to real-time ball bearing fault diagnosis.

A low area VLSI implementation of extended tiny encryption algorithm using Lorenz chaotic system

A low area VLSI implementation of extended tiny encryption algorithm using Lorenz chaotic system

On the Caputo-Fabrizio fractal fractional representation for the Lorenz chaotic system

<abstract><p>The widespread application of chaotic dynamical systems in different fields of science and engineering has attracted the attention of many researchers. Hence, understanding and capturing the complexities and the dynamical behavior of these chaotic systems is essential. The newly proposed fractal-fractional derivative and integral operators have been used in literature to predict the chaotic behavior of some of the attractors. It is argued that putting together the concept of fractional and fractal derivatives can help us understand the existing complexities better since fractional derivatives capture a limited number of problems and on the other side fractal derivatives also capture different kinds of complexities. In this study, we use the newly proposed Caputo-Fabrizio fractal-fractional derivatives and integral operators to capture and predict the behavior of the Lorenz chaotic system for different values of the fractional dimension $ q $ and the fractal dimension $ k $. We will look at the well-posedness of the solution. For the effect of the Caputo-Fabrizio fractal-fractional derivatives operator on the behavior, we present the numerical scheme to study the graphical numerical solution for different values of $ q $ and $ k $.</p></abstract>

Mitigating long transient time in deterministic systems by resetting.

How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that resetting the intrinsic dynamics intermittently to a spatial control line that passes through the equilibrium point can dramatically expedite its completion, resulting in a huge reduction in mean transient time and fluctuations around it. Moreover, our study reveals the emergence of an optimal restart time that globally minimizes the mean transient time. We corroborate the results with detailed numerical studies on two canonical setups in deterministic dynamical systems, namely, the Stuart-Landau oscillator and the Lorenz system. The key features-expedition of transient time-are found to be very generic under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer and poses open questions on the optimal way to harness transients in dynamical systems.

Fractional order PID controller for the stabilisation of chaotic systems using Takagi-Sugeno fuzzy model

In this paper, we propose a new fractional PIαDβ controller design to control chaotic systems. The controller design is based on the predictive control proposed by Yamamoto et al. (2001) and the fractional calculus. The parameters of the controller are determined by minimising the energy of the chaotic states using particle swarm optimisation. In order to obtain a simple model structure, we have used Takagi-Sugeno technique. A fractional PDβ and conventional predictive controllers have been also used as a comparative technique, in order to show the effectiveness of the proposed design one. The simulation results on Lorenz and Chen chaotic systems show the efficiency of the proposed fractional controller to reject disturbances and noises. These results show also that the fractional controller gives better results and overcome those of the fractional PDβ and conventional predictive controllers.

On-the-Fly Parallel Processing IP-Core for Image Blur Detection, Compression, and Chaotic Encryption Based on FPGA

This paper presents a 3 in 1 standalone FPGA system which can perform color image blur detection in parallel with compression and encryption. Both blur detection and compression are based on the 3-level Haar wavelet transform, which is used as a common building block to save the resources. The compression is based on performing the hard thresholding scheme followed by the Run Length Encoding (RLE) technique. The encryption is based on the 128-bit Advanced Encryption Standard (AES), which is considered one of the most secure algorithms. Moreover, the modified Lorenz chaotic system is combined with the AES to perform the Cipher Block Chaining (CBC) mode. The proposed system is realized using HDL and implemented using Xilinx on XC5VLX50T FPGA. The system has utilized only 25% of the available slices. Furthermore, the system can achieve a throughput of 3.458 Gbps, which is suitable for real-time applications. To validate the compression performance, the system has been tested with all the standard 256×256 images. It is shown that depending on the amount of details in the image, the system can achieve 30dB PSNR at compression ratios in the range of (0.08-0.38). The proposed system can be integrated with digital cameras to process the captured images on-the-fly prior to transmission or storage. Based on the application, the blurred images can be either marked for future enhancement or simply filtered out.

An Efficient Spectral Method-based Algorithm for Solving a ‎High-dimensional Chaotic Lorenz System

In this paper, we implement the multidomain spectral relaxation method to numerically study high dimensional chaos by considering the nine-dimensional Lorenz system. Chaotic systems are characterized by rapidly changing solutions, as well as sensitivity to small changes in initial data. Most of the existing numerical methods converge slowly for this kind of problems and this results in inaccurate approximations. Spectral methods are known for their high accuracy. However, they become less accurate for problems characterised by chaotic solutions, even with an increase in the number of grid points. As a result, in this work, we adopt the multidomain approach which assumes that the main interval can be decomposed into a finite number of subdomains and the solution obtained in each of the subdomains. This approach remarkably improves the results as well as the efficiency of the method.

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

A low area VLSI implementation of extended tiny encryption algorithm using Lorenz chaotic system

The rapid growing impact of light weight applications (RFID tags, smartcards, sensor nodes and FGPAs) makes security a major concern in communication systems. Light weight cryptographic algorithm or ciphers can provide security and confidentiality of data or messages transmitted. In this paper, we proposed low area VLSI implementation of extended tiny encryption algorithm using Lorenz chaotic system (XTEA-LCS method) to improve the efficiency of encryption and decryption process. The key is the major concern of the encryption and decryption process. So in this research random numbers generated using LCS was used for key purpose, which efficiently reduced area and execution time of XTEA-LCS method and improved the system security. The XTEA-LCS method has been implemented in the Xilinx tool using Verilog code on different Virtex devices such as Virtex6, Low Power Virtex-6 (LP Virtex-6), and Virtex-7. In the field programmable gate array (FPGA) implementation, the number of look up tables (LUTs), slices and flip flops reduced and the frequency increased compared to the existing methods: QTL algorithm, DROM-CSLA-QTL and XTEA. The XTEA-LCS methodology improves the FPGA performances by reducing LUTs by 82.96% and slices by 74.28% than conventional XTEA method.

Physics-informed echo state networks

We propose a physics-informed echo state network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training, which is based on the system's governing equations. The additional loss function penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system and a truncation of the Charney–DeVore system. Compared to the conventional ESNs, the physics-informed ESNs improve the predictability horizon by about two Lyapunov times. This approach is also shown to be robust with regard to noise. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.

A Novel Chaos-Based Image Encryption Scheme by Using Randomly DNA Encode and Plaintext Related Permutation

To ensure the security and privacy of digital image when its transmitting online or storing in the cloud, we proposed a novel chaos based image encryption scheme by using randomly DNA encode and plaintext related permutation. In our scheme, we first randomly encode plain image into a nucleotide sequence under the control by the piecewise linear chaotic map(PWLCM). After that, the plaintext related permutation would be done under the control sequence which generated by hyper chaotic Lorenz system (HCLS). Next, we make diffusion processing with key DNA sequence which is generated by another PWLCM system and also encoded randomly. Finally, we decode DNA sequence into cipher image matrix. In addition, we used many common security analysis methods to test our scheme, and the result compared with other works. The tests and comparison results are shown that our proposed image cryptosystem has excellent security performance to ensure the digital image security on communication.

A 2D logistic map and Lorenz-Rossler chaotic system based RGB image encryption approach

This paper presents a novel color image encryption approach. The proposed approach utilizes the basic concepts of DNA cryptography along with Lorenz and Rossler chaotic system and 2D logistic map. The proposed approach encrypts RGB images using DNA cryptography techniques. In diffusion phase, at pixel level Lorenz and Rossler chaotic system is used to encrypt the three channels of test images. Afterwards, at bit level 2D logistic map is used for performing bitwise chaotic ponytail process on these diffused Red, Green, and Blue channels in confusion phase. Simulation of the proposed approach on test images reveals that the color images have been encrypted very efficiently.

A novel combination of information hiding and confidentiality scheme

Due to exponential technological advancement, secure transmission of multimedia content is a serious challenge. These days, securing and hiding digital information most efficiently is the focus of the digital computer world. Information confidentiality and information hiding namely steganography, are the most promising techniques that can protect digital information. In this paper, a combination of encryption and steganography is used efficiently to have a double level of security to achieve confidentiality, privacy, secrecy in addition to integrity and authentication. Firstly, encryption parameters are set by using a chaotic Lorenz system (CLS), then by using CLS encryption parameter encryption is performed on the secret image. This enciphered confidential digital medium is inserted in the cover image by using the least significant bits (LSBs) steganographic scheme. Due to the double level of security, it is hard for an eavesdropper to attack the proposed scheme. All experimental and simulation results verify the efficiency of the proposed information hiding scheme.

Parallel multi-layer selector S-Box based on lorenz chaotic system with FPGA implementation

<p><span>The substitution box (S-Box) is the main block in the encryption system, which replaces the non-encrypted data by dynamic secure and hidden data. S-Box can be designed based on complex nonlinear chaotic systems that presented in recent papers as a chaotic S-Box. The hardware implementation of these chaotic systems suffers from long processing time (low speed), and high-power consumption since it requires a large number of non-linear computational models. In this paper, we present a high-speed FPGA implementation of Parallel Multi-Layer Selector Substitution Boxes based on the Lorenz Chaotic System (PMLS S-Box). The proposed PMLS chaotic S-Box is modeled using Xilinx System Generator (XSG) in 32 bits fixed-point format, and the architecture implemented into Xilinx Spartan-6 X6SLX45 board. The maximum frequency of the proposed PMLS chaotic S-Box is 381.764 MHz, with dissipates of 77 mwatt. Compared to other S-Box chaotic systems, the proposed one achieves a higher frequency and lower power consumption. In addition, the proposed PMLS chaotic S-Box is analyzed based on S-Box standard tests such as; Bijectivity property, nonlinearity, strict avalanche criterion, differential probability, and bits independent criterion. The five different standard results for the proposed S-Box indicate that PMLSC can effectively resist crypto-analysis attacks, and is suitable for secure communications.</span></p>

$\mathcal {H}_{\infty }$ Synchronization for Fuzzy Markov Jump Chaotic Systems With Piecewise-Constant Transition Probabilities Subject to PDT Switching Rule

This article investigates the nonfragile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> synchronization issue for a class of discrete-time Takagi–Sugeno (T–S) fuzzy Markov jump systems. With regard to the T–S fuzzy model, a novel processing method based on the matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of the actuator, a nonfragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this article lies in that the transition probabilities of the Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on the Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results.