Chaotic Theory Research Articles

Design of parameters for running-in cylinder liner piston rings based on running-in attractor

PurposeThe purpose of this study aims to shorten the running-in time and improve the running-in quality of cylinder liner piston rings (CLPRs), the running-in tests were carried out and running-in parameters of CLPRs were designed based on running-in attractor theory, which can guide the choice of optimal working conditions for other friction pairs.Design/methodology/approachThe running-in state and time under different working conditions are identified by the evolution law of the running-in attractor phase trajectory and fractal and chaotic characteristic quantities. The CLPRs running-in tests under different conditions were conducted and the friction signals were collected. The constructed phase trajectories and calculated chaotic parameters of the running-in attractor are obtained and the running-in state and time are identified by the evolution law of phase trajectories and chaotic characteristic quantities. The running-in quality is obtained by the surface morphology fractal dimension and characteristic roughness parameters.FindingsThe running-in parameters for short running-in time and good running-in quality are designed based on the fractal and chaotic theory and the optimal solution method are used to verify the results through the single objective or multi-objective optimization, and the corresponding optimal running-in parameters are obtained.Originality/valueThe optimal working condition parameters obtained from the design have guiding significance for the selection of CLPR running-in parameters, and this work can provide ideas for the other friction pairs.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0179/

A pursuit-evasion game robot controller design based on a neural network with an improved optimization algorithm

A pursuit-evasion game (PEG) is a type of game that utilizes one or several cooperative pursuers to capture one or several evaders. The PEG game concept has been used in different multi-robot applications such as transportation or navigation applications, search and rescue, surveillance applications such as collision avoidance and air traffic control systems, multi-defense applications such as missile guidance systems, and medical applications such as analyzing biological behaviors. Regardless of the benefits of PEG, one of the main drawbacks of such systems is the computational burden and the immense time required to learn such systems. For this reason, this work proposes a neural network game based on the pursuit-evasion game, where the leader (evader) robot tries to eat several particles/apples distributed inside a closed game environment with boundary and inner obstacles. In contrast, a follower (pursuer) robot tries to capture the leader robot and stop the particle-eating process. The leader and follower robots were designed based on a differential two-wheel robot (DTWR). The neural network is presented to control and learn the leader and follower robot directions with respect to the boundary and inside obstacles in the game environment. The neural network weights are learned using an improved sine cosine algorithm based on chaotic theory (ISCACT). The ISCACT is proposed to solve and avoid the proposed game of being trapped in the local minimum problem. The ISCACT is tested based on five multimodal benchmark functions. The ISCACT has been used in two cases, the first case arises when ISCACT is used in the follower robot’s learning process. In the second case, the ISCACT has been used in the leader robot’s learning process. The results for the first and second cases prove the superiority of the ISCACT compared with other existing works in enhancing the PEG performance time and reducing the computational burden for multi-robot applications.

Impact of Covid-19 on Early Childhood Education in Botswana

This paper examined the impact of COVID-19 on the Botswana public Early Childhood Education Programme during the pandemic in the period of 2019 - 2022. COVID-19 impacted various sectors of Botswana, the education sector included. However, the education system was not adequately prepared to cater for young learners’ education and therefore this had serious consequences on the lower levels of learning. The study adopted the qualitative approach and used the chaotic theory to guide the line of argument in the paper. Data were collected using open-ended questionnaires, structured interviews, focus group discussions and observation of outside equipment. The findings indicated a backlog of pupils entering the Early Childhood Education programme and Standard One after the Covid-19 pandemic. Standard One accepted learners of different competencies and parents refused to send their students back to school after re-opening because of fear of reinfection. The paper concludes that the Ministry of Education, like other levels of education, could have put something in place for ECE learners to keep on learning at home during the pandemic after three years of suspending teaching and learning

Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems

It is of practical significance to realize a stable and controllable financial system by using chaotic synchronization theory. In this paper, the dynamics and synchronization are studied for a class of fractional-order chaotic financial systems. First, the stability and dynamics of the fractional-order chaotic financial system are analyzed by using the phase trajectory diagram, time series diagram, bifurcation diagram, and Lyapunov exponential diagram. Meanwhile, we obtain the range of each parameter that puts the system in a periodic state, and we also reveal the relationship of the derivative order and the chaotic behaviors. Then, the adaptive control strategy is designed to achieve synchronization of the chaotic financial system. Finally, the theoretical results and control method are verified by numerical simulations.

Approximate CFTs and random tensor models

A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of ‘CFT data’. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of ‘CFT data’ satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS3 as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

A new 2D cross hyperchaotic Sine-modulation-Logistic map and its application in bit-level image encryption

Chaotic theory is being increasingly researched for application in image encryption scheme (IES). This paper presents a novel two-dimensional cross hyperchaotic Sine-modulation-Logistic map (2D-CHSLM) based on the famous Sine and Logistic maps. The hyperchaotic behaviors of 2D-CHSLM are demonstrated through bifurcation diagrams, trajectory plots, Lyapunov exponents, histogram, correlation dimension, sensitivity to initial conditions, sample entropy, 0–1 test, and NIST 800–22 test. A new bit-level IES with traditional an encryption structure is proposed utilizing 2D-CHSLM. The 2D-CHSLM-IES performs 2D-CHSLM-based bit-level confusion using a zigzag transform and 2D-CHSLM-based cross coupled diffusion operations to generate a highly secure cipher-image. Simulations and security analyses, including key space, key sensitivity, histogram, correlation, information entropy, encryption quality, known-plain and chosen-plain attacks, floating Frequency, differential attack, noise and data loss attacks, demonstrate the robust security of the proposed 2D-CHSLM-IES.

Application of Fractional-Order Multi-Wing Chaotic System to Weak Signal Detection

This work investigates a fractional-order multi-wing chaotic system for detecting weak signals. The influence of the order of fractional calculus on chaotic systems’ dynamical behavior is examined using phase diagrams, bifurcation diagrams, and SE complexity diagrams. Then, the principles and methods for determining the frequencies and amplitudes of weak signals are examined utilizing fractional-order multi-wing chaotic systems. The findings indicate that the lowest order at which this kind of fractional-order multi-wing chaotic system appears chaotic is 2.625 at a=4, b=8, and c=1, and that this value decreases as the driving force increases. The four-wing and double-wing change dynamics phenomenon will manifest in a fractional-order chaotic system when the order exceeds the lowest order. This phenomenon can be utilized to detect weak signal amplitudes and frequencies because the system parameters control it. A detection array is built to determine the amplitude using the noise-resistant properties of both four-wing and double-wing chaotic states. Deep learning images are then used to identify the change in the array’s wing count, which can be used to determine the test signal’s amplitude. When frequencies detection is required, the MUSIC method estimates the frequencies using chaotic synchronization to transform the weak signal’s frequencies to the synchronization error’s frequencies. This solution adds to the contact between fractional-order calculus and chaos theory. It offers suggestions for practically implementing the chaotic weak signal detection theory in conjunction with deep learning.

An approach for encrypting images using a four-dimensional logistic map

Encrypting image transmission has been one of the most complex challenges with communication technology ever. Millions of people utilize and share photographs via the internet for personal and professional purposes. One approach to secure picture transfer over the network is to use encryption techniques to transform the original picture into an unreadable or garbled version. Several novel and encouraging possibilities for creating secure Image data encryption techniques are presented by cryptographic algorithms grounded in chaotic logistic theory. Developing a foolproof method for encrypting both black-and-white and color image is the primary focus of this work. Both grayscale and color images can be encrypted using the keys generated by combining the chaotic logistic with the image's density in the first stage of the proposed system's encryption process. The original image can then be recovered in the second stage, which is the inverse of the encryption process. Two publicly available standard grayscale and color photographs were analyzed to evaluate the suggested approach. Peak signal-to-noise ratio (PSNR), unified average changing intensity (UACI), and number of pixels change rate (NPCR) were found to be 6.6268, 51.3011, and 100, respectively, according to the test findings.

Study of Chaotic-based Audio Encryption Algorithms: A Review

Nowadays, multimedia communication has become very widespread and this requires it to be protected from attackers and transmitted securely for reliability. Encryption and decryption techniques are useful in providing effective security for speech signals to ensure that these signals are transmitted with secure data and prevent third parties or the public from reading private messages. Due to the rapid improvement in digital communications over the recent period up to the present, the security of voice data transmitted over various networks has been classified as a favored field of study in earlier years. The contributions to audio encryption are discussed in this review. This Comprehensive review mainly focuses on presenting several kinds of methods for audio encryption and decryption the analysis of these methods with their advantages and disadvantages have been investigated thoroughly. It will be classified into encryption based on traditional methods and encryption based on advanced chaotic systems. They are divided into two types, continuous-time system, and discrete-time system, and also classified based on the synchronization method and the implementation method. In the fields of information and communications security, system designers face many challenges in both cost, performance, and architecture design, Field Programmable gate arrays (FPGAs) provide an excellent balance between computational power and processing flexibility. In addition, encryption methods will be classified based on Chaos-based Pseudo Random Bit Generator, Fractional-order systems, and hybrid chaotic generator systems, which is an advantageous point for this review compared with previous ones. Audio algorithms are presented, discussed, and compared, highlighting important advantages and disadvantages. Audio signals have a large volume and a strong correlation between data samples. Therefore, if traditional cryptography systems are used to encrypt such huge data, they gain significant overhead. Standard symmetric encryption systems also have a small key-space, which makes them vulnerable to attacks. On the other hand, encryption by asymmetric algorithms is not ideal due to low processing speed and complexity. Therefore, great importance has been given to using chaotic theory to encode audio files. Therefore, when proposing an appropriate encryption method to ensure a high degree of security, the key space, which is the critical part of every encryption system, and the key sensitivity must be taken into account. The key sensitivity is related to the initial values and control variables of the chaotic system chosen as the audio encryption algorithm. In addition, the proposed algorithm should eliminate the problems of periodic windows, such as limited chaotic range and non-uniform distribution, and the quality of the recovered audio signal remains good, which confirms the convenience, reliability, and high security.

Optimizing berth-crane allocation considering tidal effects using chaotic quantum whale optimization algorithm

With the normalization of the global epidemic, shipping has gradually resumed, resulting in a surge in port throughput. Terminal managers are having great difficulty in making container ports be stable, orderly, and efficient. For small and medium-sized ports, making full use of the tidal water level to increase the operation time of large ships significantly improves the efficiency of port operations. Therefore, considering the impact of tidal factors on the operation of container ports, this paper firstly proposes a new berths and quay cranes allocation optimization model, T-B&QC, that minimizes the distance between the actual berthing berth and the preferred berth, the port time cost of ships and the number of quay crane movements as the optimization objectives, under constraints that consider tidal factors. Then, to solve the T-B&QC model using chaotic mapping and quantum theory, the Whale Optimization Algorithm (WOA) is integrated by using the Chaotic Quantum Rotating Gate Algorithm (CQRGA) and the Quantum Not Gate Algorithm (QNGA), whale coding rules are designed, and the Feasible-Integer Processing Algorithm (WF-IP) is established. Afterwards, the Chaotic Quantum Whale Optimization Algorithm, CQWOA, is proposed. Finally, the CQWOA is used to develop a new berth and quay crane allocation optimization method, T-B&QC_CQWOA. Subsequently, data from an actual seaport container port is used to test the reliability and superiority of the proposed distributing approach and the established optimizing algorithm. Numerical results demonstrate that the proposed distributing approach outperforms the classical distribution models that are selected herein, and the CQWOA yields a coordinated schedule of higher quality than the others in the process of solving the model.

Qualitative Properties of a Physically Extended Six-Dimensional Lorenz System

In this paper, the qualitative properties of a physically extended six-dimensional Lorenz system, with additional physical terms describing rotation and density, which was proposed in [Moon et al., 2019] have been investigated. The dissipation, invariance, Lyapunov exponents, Kaplan–Yorke dimension, ultimate boundedness and global attractivity of this six-dimensional Lorenz system have been discussed in detail according to the chaotic systems theory. We find that this system exhibits chaos phenomena for a new set of parameters. It is well known that the general method for studying the bounds of a chaotic system is to construct a suitable Lyapunov-like function (or the generalized positive definite and radically unbounded Lyapunov function). However, the higher the dimension of a chaotic system, the more difficult it is to construct the Lyapunov-like function. The innovation of this paper is that we first construct the suitable Lyapunov-like function for this six-dimensional Lorenz system, and then we prove that this system is not only globally bounded for varying parameters, but it also gives a collection of global absorbing sets for this system with respect to all parameters of this system according to Lyapunov’s direct method and the optimization method. Furthermore, we obtain the rate of the trajectories going from the exterior to the global absorbing set. Some numerical simulations are presented to validate our research results. Finally, we give a direct application of the results obtained in this paper. According to the results of this paper, we can conclude that the equilibrium point [Formula: see text] of this system is globally exponentially stable.

Research on optimization method for traffic signal control at intersections in smart cities based on adaptive artificial fish swarm algorithm

The transportation environment of smart cities is complex and ever-changing, and traffic flow is influenced by various factors. With the increase of traffic flow in smart cities, optimizing traffic intersection signal control has become an important method to improve traffic efficiency and reduce congestion. To this end, a smart city traffic intersection(SCTI) signal control optimization method based on adaptive artificial fish swarm algorithm was studied. Establish the Equation of state of traffic flow at SCTIs to understand the actual traffic flow at SCTIs. On this basis, design SCTI signal control parameters, with the minimum average delay and average number of stops as objective functions, and construct an optimization model for SCTI signal control. By combining chaotic search theory and adaptively improving the artificial fish swarm algorithm, based on the adaptive artificial fish swarm algorithm, the intelligent city traffic intersection signal control optimization model is solved to achieve intelligent city traffic intersection signal control optimization. The experimental results show that the average delay of this method is 7.8 ms, the average number of stops is 2, and the travel time is 68.4 s s. Thus, it is proved that the method in this paper has a good optimization effect of traffic signal control at smart city intersections, which can improve the optimization efficiency of traffic signal control at smart city intersections and reduce traffic congestion at smart city intersections.

Optimisation design of child seat based on chaos mutation MOPSO

To improve the safety of the children in child seats when a vehicle collision occurs, a finite element model of a child safety seat is established, and LS-DYNA is used for crash simulation. Select backrest inclination, headrest inclination, and seat belt centre height as design variables to establish response surface models. The application of chaotic mutation theory in particle swarm optimisation (PSO) is proposed, and the optimal solution of child seat parameters is obtained by using the chaotic mutation based grouped multi-objective particle swarm optimisation (MOPSO). The optimal solution was used to carry out the simulation experiment again, and compared with the original performance. It turned out that the Head Performance Criterion (HPC) is 47.08% better than the original child seat. Besides, the rib deformation is reduced by 21.30%, the neck shear stress is reduced by 55.74%, and the thigh stress is reduced by 48.55%, which indicate significant improvements. The results suggest that a certain parameter combination of the child seat leads to the optimal overall performance in child injury prevention, which indicates significant improvement in the damage of all parts of the child.

Numerical investigation of induction of chaotic micromixing via vibration switching

Enhanced mixing in microfluidic systems is necessary in many applications such as chemical processing, biological assays, and diagnosis. We are developing a microfluidic system to efficiently mix minute reagents (down to several microliters) using vibration-induced flow (VIF), in which a net flow is generated around a micropillar by applying periodic vibration. In this study, we numerically investigate the enhancement in chaotic mixing using the VIF technique and periodic switching of vibrations. By extending our previous numerical simulation model, we investigate the flow field and trajectories of fluid particles in three-dimensional space. We demonstrate that chaotic advection characteristics can be observed by periodically switching the vibrational direction of a substrate using simple cylindrical pillars. In addition, using an appropriate interval for switching the vibration axes yields better mixing performance. The extent of chaotic advection is evaluated quantitatively using the Lyapunov exponent considering various vibration parameters, such as the vibration amplitude, separation distance between each pillar and pillar shape. The flow field induced by a large-amplitude and sharp-edged wall pillar provides excellent mixing results. Thus, VIF is successfully applied to obtain an efficient mixing strategy with the aid of the chaotic theory.

Protecting Sensitive Images with Improved 6-D Logistic Chaotic Image Steganography

In the digital age, strong methods for safeguarding sensitive data are essential. Image steganography is a practical technique for data protection that hides information inside seemingly authentic images. The proposed method increases security by using chaotic based image encryption and decryption. Encryption approaches based on chaotic logistic theory present an abundance of attractive and novel opportunities for developing secure image encryption methods. Nevertheless, these maps are frequently used for specific, unpredictable starting parameters. This problem is addressed by the research's Tabu search optimisation method. This method optimises chaotic map initial settings using a fitness function with numerous objectives. For image encryption, the most efficient methods are used to produce confidential keys. The input picture undergoes horizontal and vertical diffusion and permutation during encryption. These operations further scramble the image data, making it even more difficult to detect the hidden information. The primary goal is to develop a safe method for encrypting both color and grayscale images. Two common grayscale and color images that are accessible to the public were used to test the suggested strategy. compare our method with key existing works, specifically on the basis of Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Peak Signal-to-Noise Ratio (PSNR) and speed, respectively, our approach improves upon these studies. Our results demonstrate that 7.9981, 99.8245, 35.6507, and 78.871 are the greatest values of entropy, NPCR, UACI, and PSNR, respectively. Whereas the respective speeds of encryption and decryption increase to 0.8433 and 1.4387 seconds. This innovative approach presents a powerful tool for applications requiring secure image steganography

Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos

We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a ‘linear ramp’). We ‘bootstrap’ the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity.

An anatomization of pulse solitons of nerve impulse model via phase portraits, chaos and sensitivity analysis

Across the neuronal membrane, the Korteweg–de Vries equation regulates the spatial and temporal development of the density difference among extracellular and intracellular liquids. In this study, model of the nerve impulse is taken into consideration by means of bifurcation and chaotic theory. The considered model is subjected to an extended direct algebraic method, that revealed abundant analytical results containing hyperbolic, trigonometric and rational functions. Solitons are obtained in terms of pulse stimulation from density difference equation. These results are made accessible together with their fundamental requirements, which ensure the continuance of pulse solitons such as dark, singular and kink that utilize suitable physical parameters in 2D plots. Subsequently, the nonlinear density difference equation is transformed into a planar dynamical system via a Galilean transformation. Bifurcation theory is applied to the dynamical structure of the considered setup to investigate the possible phase portraits of the travelling wave results. Furthermore, we applied the numerical approaches to determine the periodic and quasiperiodic behaviours of the considered equation and the findings are exhibited graphically. Sensitivity and multistability analysis are additionally used to study the periodic and quasiperiodic behaviour for several initial constraints. At the end, the concluding remarks are presented.

Exploring market instability of global lithium resources based on chaotic dynamics analysis

Driven by emerging technologies such as batteries in electric vehicles (EVs), global lithium market undergoes significant changes. To explore market instability of global lithium resources subjected to EV development, lithium exploration, and carbon constraints, a model of global lithium markets-electric vehicle development-carbon constraints (GL-EV-CC) is established based on a four-dimensional difference equation feedback system. Accordingly, a detailed analysis strategy by virtue of bifurcation and chaotic theory is investigated, with which some sudden changes and critical points can be obtained to provide some implications in face of the challenges of future market changes. Results show that lithium demand for EVs will evolve from an equilibrium state to a periodic state and finally to a chaotic state with the continuous change of the degree of investment in Research and Development (R&D) of EVs. When the degree of exploration is less than 0.15, attention should be given to the resource exhausted crisis. When the degree of carbon constraint is high, market instability of lithium demand should be fairly concerned, while when the degree of carbon constraint is low, market instability of lithium supply should be focused. Unlike previous studies, chaotic dynamic analysis is employed in this study, and thereby not only a broader sensitivity analysis but also complex dynamic behaviors such as chaotic behavior at the moment of equilibrium can be explored, in which feasible policies can be proposed to control some policy parameters to be within a reasonable range.

Foreword to the special issue of Journal of Difference Equations and Applications on ‘Lozi, Hénon, and other chaotic attractors, theory and applications’

This foreword presents the 32 articles of the special issue devoted to the Lozi, Hénon and other chaotic attractors proposed by 78 authors from 20 countries (Algeria, Brazil, Canada, China, Czech Republic, France, Germany, India, Italy, Jamaica, Japan, Lebanon, New Zealand, Portugal, Russia, Saudi Arabia, Spain, Ukraine, Tunisia, USA). These original research papers consider chaotic attractors, both in their theoretical and applied aspects.

Attacks on Recent DNN IP Protection Techniques and Their Mitigation

With the rapid increase in the development of Deep Learning methodologies, Deep Neural Networks (DNNs) are now being commonly deployed in smart systems (e.g. autonomous vehicles) and high-end security applications (e.g. face recognition, biometric authentication, etc.). The training of such DNN models often requires exclusive valuable training datasets, enormous computational resources, and expert fine-tuning skills. Hence, a trained DNN model can be regarded as valuable proprietary Intellectual Property (IP). Piracy of such DNN IPs has emerged as a major concern, with increasing trends of illegal copying and redistribution. A number of mitigation approaches targeting DNN IP protection have been proposed in recent years. In this work, we target two recently proposed DNN IP protection schemes: (a) Chaotic Map theory based encryption of the weight parameters, and (b) traditional block cipher based encryption of the weights. We demonstrate attacks on two recent DNN IP protection techniques, with one technique each belonging to the above-mentioned schemes, under a pragmatic attack model. We also propose a novel DNN IP protection technique based on selective encryption of the weight parameters, termed LEWIP to mitigate the exposed weaknesses, while having low implementation and performance overheads. Finally, we demonstrate the effectiveness of the LEWIP technique against state-of-the-art DNN implementations.