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It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis. • A new formulation on semi-analytical time-domain model for fluidelastic instability of tube bundles. • The formulation has explicit fluid force expressions. • Linear frequency- and time-domain analysis are validated against available experimental and theoretical results. • Nonlinear dynamics behavior of a loosely-supported tube is probed based on the new formulation by using various techniques. • The route to chaos of the system is found through quasi-periodic to chaos. [ABSTRACT FROM AUTHOR]

The present paper provides a historical context for chaos theory, originating in the 1960s with Edward Norton Lorenz's efforts to predict weather patterns. It introduces chaos theory, fractal geometry, nonlinear dynamics, and the butterfly effect, highlighting their exploration of complex systems. The authors aim to bridge the gap between chaos theory and oral and maxillofacial surgery (OMFS) through a literature review, exploring its applications and emphasizing the prevention of minor deviations in OMFS to avoid significant consequences. A comprehensive literature review was conducted on PubMed, Web of Science, and Google Scholar databases. The selection process adhered to the PRISMA-ScR guidelines and Leiden Manifesto principles. Articles focusing on chaos theory principles in health sciences, published in the last two decades, were included. The review encompassed 37 articles after screening 386 works. It revealed applications in outcome variation, surgical planning, simulations, decision-making, and emerging technologies. Potential applications include predicting infections, malignancies, dental fractures, and improving decision-making through disease prediction systems. Emerging technologies, despite criticisms, indicate advancements in AI integration, contributing to enhanced diagnostic accuracy and personalized treatment strategies. Chaos theory, a distinct scientific framework, holds potential to revolutionize OMFS. Its integration with advanced techniques promises personalized, less traumatic surgeries and improved patient care. The interdisciplinary synergy of chaos theory and emerging technologies presents a future in which OMFS practices become more efficient, less traumatic, and achieve a level of precision never seen before. [ABSTRACT FROM AUTHOR]

The security of patient data is a critical problem for health networks due to the rising popularity of telehealth services and the requirements for clinical data sharing between surgeons, consultants, and medical groups. In contrast to protecting medical data, which includes the cover (i.e., clinical picture), the requirements for protecting other pertinent data are more general. The paper advocates for data encryption before concealment as a robust strategy to uphold patient privacy during medical information exchange. The primary focus of this analysis revolves around a comprehensive exploration of different steganography methods. Through a meticulous examination of various steganographic techniques, including LSB, PVD, and transform domain approaches, this paper provides a detailed analysis of their strengths and limitations. Objective metrics like PSNR and SSIM are employed to dissect the trade-offs between data security and visual fidelity. The research leads to the conclusion that the diagonal queue-based steganog-raphy methodology, supported by chaotic methods, the Linear Feedback Shift Register (LFSR), and the durable Rabin encryption system, is the best course of action. This method enables autonomous data transmission among numerous contacts while ensuring the highest level of confidentiality and integrity of patient data inside e-health networks. In summary, this study provides a comprehensive solution that protects patient data and speeds data transmission inside the expanding framework of e-health networks in order to meet urgent data security concerns in telemedicine and healthcare data exchange. [ABSTRACT FROM AUTHOR]

• A wider class of homogeneous spacetimes can be described using General Relativity. • The models are categorized into Bianchi I to IX, by employing Lie Algebras. • We explore several inflationary Mixmaster models by using potential inflaton fields. • Inflation affects the stability of the Bianchi IX model, which becomes more stable. The objective of this research is to investigate the dynamical behavior of the Bianchi IX Universe through various inflationary models induced by scalar fields. Specifically, we explore potentials for the inflaton field of the form V (ϕ) ∝ ϕ δ , where c varies from 1 to 4. To discern any chaotic behavior in the system, we calculate basin diagrams using the smaller alignment index (SALI) and the grid classification method. The fractal nature of the basins is evaluated through the utilization of two distinct indicators, namely the box-counting dimension and the boundary basin entropy. Our findings reveal that the inflaton affects the stability of the Bianchi IX model, which is intrinsically chaotic and becomes more stable as the power of the scalar-field potential increases. Moreover, except in the case δ = 1 , the impact of the scalar field on the dynamics is independent of the exponent δ. [ABSTRACT FROM AUTHOR]

Principal Component Analysis (PCA) is a widely used technique for fault detection and diagnosis. PCA works well when the data set has linear characteristics. However, most industrial processes have nonlinear characteristics in their data. Kernel PCA (KPCA) is an alternative solution for such types of data sets. This solution doesn't come without a cost since one of KPCA's disadvantages is a large number of observations which results in more occupied storage space and more execution time than the PCA technique. Furthermore, if the data is too large it may minimize the monitoring performance of the KPCA model. Reduced KPCA (RKPCA) is a solution for the conventional KPCA limitations. Firstly, RKPCA can deal with nonlinear characteristics without crucial problems because it is based on the KPCA algorithm with a data reduction part where it keeps most of the data's information. Thus, by reducing the number of observations RKPCA reduces the occupied storage space and execution time while preserving tolerable monitoring performance. The proposed RKPCA algorithm consists of two parts. First, the large-sized training data set is reduced using the fractal dimension technique (correlation dimension). Afterward, the KPCA model is developed through the obtained reduced training data set. The proposed scheme is applied to the Tennessee Eastman Process and the Cement Plant Rotary Kiln data sets to evaluate its performance in comparison with other algorithms. [ABSTRACT FROM AUTHOR]

This article introduces a novel model of asymmetric neural networks combined with fractional difference memristors, which has both theoretical and practical implications in the rapidly evolving field of computational intelligence. The proposed model includes two types of fractional difference memristor elements: one with hyperbolic tangent memductance and the other with periodic memductance and memristor state described by sine functions. The authenticity of the constructed memristor is confirmed through fingerprint verification. The research extensively investigates the dynamics of a coupled neural network model, analyzing its stability at equilibrium states, studying bifurcation diagrams, and calculating the largest Lyapunov exponents. The results suggest that when incorporating sine memristors, the model demonstrates coexisting state variables depending on the initial conditions, revealing the emergence of multi-layer attractors. The article further demonstrates how the memristor state shifts through numerical simulations with varying memductance values. Notably, the study emphasizes the crucial role of memductance (synaptic weight) in determining the complex dynamical characteristics of neural network systems. To support the analytical results and demonstrate the chaotic response of state variables, the article includes appropriate numerical simulations. These simulations effectively validate the presented findings and provide concrete evidence of the system's chaotic behavior. [ABSTRACT FROM AUTHOR]

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial Neural Networks (DANN) are very popular in our days. Depending on the learning task, the exact form of DANNs is determined via their multi-layer architecture, activation functions and the so-called loss function. However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions. In the current paper, we suggest to analyze the neural signal processing in DANNs from the point of view of homogeneous chaos theory as known from polynomial chaos expansion (PCE). From the PCE perspective, the (linear) response on each node of a DANN could be seen as a 1st degree multi-variate polynomial of single neurons from the previous layer, i.e. linear weighted sum of monomials. From this point of view, the conventional DANN structure relies implicitly (but erroneously) on a Gaussian distribution of neural signals. Additionally, this view revels that by design DANNs do not necessarily fulfill any orthogonality or orthonormality condition for a majority of data-driven applications. Therefore, the prevailing handling of neural signals in DANNs could lead to redundant representation as any neural signal could contain some partial information from other neural signals. To tackle that challenge, we suggest to employ the data-driven generalization of PCE theory known as arbitrary polynomial chaos (aPC) to construct a corresponding multi-variate orthonormal representations on each node of a DANN. Doing so, we generalize the conventional structure of DANNs to Deep arbitrary polynomial chaos neural networks (DaPC NN). They decompose the neural signals that travel through the multi-layer structure by an adaptive construction of data-driven multi-variate orthonormal bases for each layer. Moreover, the introduced DaPC NN provides an opportunity to go beyond the linear weighted superposition of single neurons on each node. Inheriting fundamentals of PCE theory, the DaPC NN offers an additional possibility to account for high-order neural effects reflecting simultaneous interaction in multi-layer networks. Introducing the high-order weighted superposition on each node of the network mitigates the necessity to introduce non-linearity via activation functions and, hence, reduces the room for potential subjectivity in the modeling procedure. Although the current DaPC NN framework has no theoretical restrictions on the use of activation functions. The current paper also summarizes relevant properties of DaPC NNs inherited from aPC as analytical expressions for statistical quantities and sensitivity indexes on each node. We also offer an analytical form of partial derivatives that could be used in various training algorithms. Technically, DaPC NNs require similar training procedures as conventional DANNs, and all trained weights determine automatically the corresponding multi-variate data-driven orthonormal bases for all layers of DaPC NN. The paper makes use of three test cases to illustrate the performance of DaPC NN, comparing it with the performance of the conventional DANN and also with plain aPC expansion. Evidence of convergence over the training data size against validation data sets demonstrates that the DaPC NN outperforms the conventional DANN systematically. Overall, the suggested re-formulation of the kernel network structure in terms of homogeneous chaos theory is not limited to any particular architecture or any particular definition of the loss function. The DaPC NN Matlab Toolbox is available online and users are invited to adopt it for own needs. • Kernel structure reformulation of deep artificial neural networks in terms of homogeneous chaos theory. • Response on each node of the deep network represented through polynomial chaos expansion. • Orthonormal decomposition mitigates the non-optimal representation while processing the neural signal. • Accounting for high-order effects reflecting simultaneous neural impacts. • Analytical estimation of mean and variance of neural signal on each node is provided. [ABSTRACT FROM AUTHOR]

The parameter range of traditional 2D chaotic maps is small, limiting the sequence generation performance. In order to improve security and efficiency, it is necessary to develop a new 2D chaotic map for image encryption. This paper proposes an enhanced version of the Henon Map, called 2D-HHMSC, which has better sequence generation performance than the Henon Map under the same parameters. In addition, 2D-HHMSC has ample parameter space, enhancing the generated sequences' randomness. The proposed method is a new color image encryption algorithm. To prevent the algorithm from being subjected to brute force attacks, two hash functions are used to generate the parameters and initial values of the Arnold map and 2D-HHMSC. The key space of the algorithm can reach 2̂1024. In the scrambling phase, the three channels of the color image are scrambled using Arnold maps with different parameters and then combined into a grayscale image. In order to fully diffuse the scrambled image, use the key stream generated by 2D-HHMSC to diffuse the grayscale image, starting from the center position of the grayscale image The correlation coefficients of the proposed encryption algorithm are 0.002, 0.0012, and −0.0006, and the information entropy is 7.9993. Experimental results show that the algorithm can resist common attacks, proving its robustness and reliability. [ABSTRACT FROM AUTHOR]

• Constructing pseudo-Hamiltonian system, the topology of dynamic motion is able to distinguish whether the system is in chaos. • The fractal process of the attraction basin verifies the chaotic distribution solved by Melnikov function. • Larger force fluctuation leads to the critical point hysteresis of damping and average force occurring bifurcation or chaos. • The quantitative optimal couple of structural with process parameters determine the priority of the parameter control. This paper investigates the stability of horizontal nonlinear vibration of four-high cold mill under the effects of gyro-precession and eccentricity between rolls. The threshold value of chaos about Smale horseshoe commutation is given from Melnikov method, and the correctness of the result is verified by the fractal process of the attraction basin. Through the analyzes of bifurcation, maximum Lyapunov exponents and bi-parameter bifurcation, it is revealed for the effect of different parameters variation on the nonlinear dynamic behavior of horizontal vibration in rolling system. The results show, the fluctuation amplitude of horizontal force increases, the stable domain decreases, and once its value ≥3.5, it is necessary to prefer to the adjustment of parameter-exciting stiffness; meanwhile, it is noticeable that the critical points of damping and average force of the system with bifurcation or chaos appear hysteresis. The evolutions of system dynamics with four pairs of parameter changes confirm the quantitative optimal couple of one structural plus one process parameter in the system. Based on this, we can also find a balance between the average horizontal force and eccentricity, so as to optimize the structural design so that there is a proper and reliable eccentricity between the rolls. The results provide a theoretical reference for service stability and dynamic reliability of the rolling mill system. [ABSTRACT FROM AUTHOR]

In 1980 Richard H. Day co-founded and long edited the Journal of Economic Behavior and Organization (JEBO). It development reflected the intellectual journey that Day himself followed in his career from an early interest in decision-making by farmers using programming methods through studying adaptation in organizations facing bounded rationality and nonlinear dynamics to a broad evolutionary approach to long-run patterns of economic growth and development. A not widely recognized outcome of this was that JEBO would become a leading outlet for evolutionary economics, including all of its various strands, including biological, organizational, NeoSchumpeterian, Alchian efficiency, Simonian bounded rationality, evolutionary game theory, and complexity evolution. [ABSTRACT FROM AUTHOR]

In this research, the model under consideration is the Fokas system that simulates the dynamics of wave through single mode fiber optics. Dark, bright, kink and periodic optical solitons are yielded using Painlevé approach and semi-inverse variational principle. The constraint conditions for the existence of the solutions also merge during the derivation. The obtained solutions are discussed to depict and support theoretical outcomes through the phase portraits. Further, we have applied the idea of bifurcation and chaos theories to get a better understanding of the planar dynamical system obtained from the studied system. The chaotic solutions for the perturbed dynamical system are also obtained and displayed through graphs. The sensitivity analysis of the model is also investigated, and the results show that the given model is not highly sensitive and is stable. These unique ideas employ symbolic computations to provide dynamical as well as potent mathematical tool related to tackling diverse benign nonlinear wave problems. The dynamics analysis method and numerical results are meaningful and helpful to further study on the reliability control of Fokas system. [ABSTRACT FROM AUTHOR]

This paper studies the synchronization behavior of multistable chaotic systems with coexisting symmetric attractors. Specifically, the focus is on the attractive and repulsive couplings of the attractors in single-variable couplings. It is shown that in the self-couplings, both attractors have the same synchronization pattern either in the attractive or repulsive coupling. In the cross-couplings, the synchronization pattern of the attractors is dependent on the variables involved in the coupling and the symmetry transformation. If the coupling scheme is defined such that only one of the variables in the coupling participates in the symmetry transformation, the synchronization patterns of the symmetric attractors are symmetric in the attractive and repulsive couplings. The master stability function is applied to four chaotic systems with different symmetry transformations to represent the results. The corresponding chaotic circuit of two coupled symmetric systems is also implemented and their symmetric responses are shown. • Synchronization stability of coexisting symmetric chaotic attractors is investigated. • Coupling is considered to be both attractive and repulsive through single variable. • In self-couplings, symmetric attractors have the same synchronization patterns. • symmetry synchrony is observed if one transformation variable is in the coupling. [ABSTRACT FROM AUTHOR]

Taking kidney bean as the research object, row spacing, fertilizer application and planting density were selected as experimental factors, production for the response indicators, the chaos theory, krill herd algorithm is introduced into the BP neural network, the minimum error in training as a target, the model of weight and threshold as variables to optimize the BP neural network and chaotic krill herd algorithm BP neural network prediction model was set up (C-KHA-BP). The RMSE of C-KHA-BP model is 191.93 kg/hm2、MAE is 153.18 kg/hm2, and MAPE is 12.67%, the correlation coefficient R2 is 0.95.By solving the global optimal solution of C-KHA-BP model, the optimal row spacing of kidney bean was 72.63 cm, the fertilizer application rate was 103.91 kg/hm2, and the planting density was 30 × 104 plants /hm2. The next year, the validation test was conducted in the same test area, and the yield of kidney bean under the test scheme was 2843.2 kg /hm2, the relative error between the test result and the simulation optimization result (2949.5 kg /hm2) was only −3.65%, indicating that the fitting function of C-KHA-BP prediction model was precision and the optimization result was accurate. The results of this study can provide a new approach to the prediction and optimization of similar models in the field of grain production. [ABSTRACT FROM AUTHOR]

[Display omitted] • Shape and size Optimization of truss Structures is considered. • Chaos Game Optimization (CGO) is utilized for optimization purposes. • Benchmark 10-bar, 37-bar, 52-bar, 72-bar and 120-bar truss structures are utilized. An engineering system consists of properly established activities and put together to achieve a predefined goal. These activities include analysis, design, construction, research, and development. Designing and constructing structural systems, including buildings, bridges, highways, and other complex systems, have been developed over the centuries. However, the evolution of these systems has been prolonged because the overall process is very costly and time-consuming, requiring primary human and material resources to be utilized. One of the options for overcoming these shortcomings is the utilization of metaheuristic algorithms as recently developed intelligent techniques. These algorithms can be utilized as upper-level search techniques for optimization procedures to achieve better results. Shape and size optimization of truss structures are considered in this paper utilizing the Chaos Game Optimization (CGO) as one of the recently developed metaheuristic algorithms. The principles of chaos theory and fractal configuration are considered inspirational concepts. For the numerical purpose, the 10-bar, 37-bar, 52-bar, 72-bar, and 120-bar truss structures as four of the benchmark problems in this field are considered as design examples in which the frequency constraints are considered as limits that have to be dealt with during the optimization procedure. Multiple optimization runs are also conducted for having a comprehensive statistical analysis, while a comparative investigation is also conducted with other algorithms in the literature. Based on the results of the CGO and other approaches from the literature, the CGO can provide better and competitive results in dealing with the considered truss design problems. In summary, the CGO can provide better solutions in dealing with the considered real-size structural design problems with higher levels of complexity. [ABSTRACT FROM AUTHOR]

Chaos theory is a mathematical theory that studies nonlinear dynamical systems and has found extensive applications in the disease auxiliary diagnosis. FTIR spectra is a technique based on infrared spectroscopy that provides information about molecular vibrations, rotations, and vibrational-rotational energy levels by recording the absorption spectrum of a sample in the infrared radiation range. This technology has gained attention for its extensive applications in the disease auxiliary diagnosis. However, due to the limited amount of molecular information captured by FTIR spectra and intricate clinical diagnostic scenarios, this study introduces an innovative approach by combining FTIR spectra with chaos theory. This novel method for disease prediction is proposed and validated using FTIR spectra datasets from various diseases, including glioma, non-small cell lung cancer (NSCLC), and systemic lupus erythematosus (SLE). The experimental results demonstrate that the proposed Low-rank Tensor Features Fusion-BiGRU (LTFF-BiGRU) model achieves competitive outcomes in three datasets. Comparing the spectral features, inputting spectral-chaotic fusion features into LTFF-BiGRU models can effectively improve the average Accuracy (Acc) by 3.5 %, average Precision (Pre) by 3.30 %, average Sensitivity (Sen) by 2.37 %, average Specificity (Spe) by 4.07 %, average F1 score by 3.10 %, and average Area Under the ROC Curve (AUC) by 3.23 %. Through low-rank tensor fusion, the correlations and interaction patterns between different feature data can be effectively captured, thus extracting a more comprehensive and enriched feature representation to enhance disease diagnosis results further. This research marks the first demonstration of chaotic characteristics in FTIR spectra and pioneers the exploration of employing low-rank tensor fusion between spectral features and chaotic features. The research signifies a crucial step in integrating FTIR spectra with chaos theory in the disease auxiliary diagnosis, paving the way for further exploration in this promising interdisciplinary field. [Display omitted] • The first proof of chaotic characteristics in FTIR spectra. • The first proof of the value of combining FTIR spectra with chaos theory. • Employing low-rank tensor fusion for spectral and chaotic features combination. • The proposed LTFF-BiGRU model achieved competitive results. [ABSTRACT FROM AUTHOR]

• A novel audio encryption approach is proposed that uses DNA computing and RCM chaotic map. • A new pseudorandom bit generation approach is proposed that is used for audio encryption purposes. • DNA-based parallelism translates to faster encryption and decryption processes, a crucial aspect for real-time audio applications like video conferencing. • A new-term "AUDEL" is coined in this work which is an abbreviation of the AUDio ELements. Fig. 4 illustrates the construction of the AUDEL matrix from the stereo audio data that helps in designing an efficient audio encryption framework. • A new scrambling approach is proposed that applies the RCM chaotic map and the proposed pseudorandom bit sequence generator. In this work, an audio encryption framework is proposed based on the chaos theory and DNA encoding. Traditional encryption algorithms designed for text data might not be efficient for handling the bulk data of audio files, leading to slow processing times and increased storage requirements. Striking the right balance between robust encryption and efficient processing is crucial. Additionally, some encryption methods can introduce noise or artifacts into the audio signal, impacting its clarity. Maintaining high-fidelity audio quality while ensuring strong encryption remains an ongoing area of research. Despite these challenges, the need for secure audio communication is undeniable. The RCM chaotic map is used to introduce chaotic properties in the encryption framework. A novel pseudorandom bit generator approach is proposed and used for encryption purposes. The proposed work is a symmetric encryption approach and is completely lossless. The proposed approach uses some lightweight computational procedures that make the algorithm simple and computationally less expensive which makes it suitable for real-time applications. Furthermore, the proposed approach shows significant performance and resilience against various cryptographic attacks. A new scrambling algorithm is proposed to add a layer of security. The proposed scramble algorithm uses logistic map beside the RCM map. The proposed approach achieved 98.28 % NSCR value and 33.63 % UACI values on average. The experimental outcomes are encouraging for practical applications of the proposed approach. [ABSTRACT FROM AUTHOR]

Ethnic and religious conflicts frequently evolve into highly explosive situations marked by the sudden eruption of conflictive mass behaviour in the form of leaderless protests or riots. In this article, we introduce a new theoretical approach, the forest-fire model of cultural identity conflict escalation (FFM). The model offers a fresh perspective on conflict dynamics by focusing on the nonlinear dynamics inherent in self-organized collective mass behaviour in ethnic and religious conflicts. It serves to overcome the dominance of rationalist elite-centred and structuralist-institutionalist approaches in the field. We conceptualize conflictive mass behaviour as avalanching "cascades" to facilitate an understanding of the complex dynamics of ethnic and religious upheavals. The FFM unites time-invariant antecedent conditions of conflictive mass behaviour with extremely time-variant triggering events. According to the model, an emboldening emotional climate, characterized by a blend of shared anger, pride and hope, provides the "fuel" that is sparked by a disruptive incident. By integrating collective emotions, triggering events, and leaderless self-organization, the model offers an innovative and substantiated elucidation of the nonlinear, short-term escalation dynamics of collective mass behaviour in cultural identity conflicts. • The article introduces the forest-fire model of cultural identity conflict escalation (FFM). • Ethnic and religious upheavals exhibit a highly dynamic, self-organized, and nonlinear nature. • Ethnic upheavals are set in motion by seemingly insignificant triggering events. • The critical determinant for the intensity of an upheaval wave lies in a emboldening emotional arousal. [ABSTRACT FROM AUTHOR]

A new three-dimensional Jerk chaotic system with line equilibrium points is proposed. The system is researched in detail by the Lyapunov exponent graph, bifurcation diagram, phase diagram, and time domain waveform diagram, which show that the system has rich dynamical behaviors, such as eight types of coexisting attractors, extreme multistability of four different attractor states, and offset boosting in two directions. In addition, the system also has six types of transient chaos, which greatly increase the complexity of the system. We study the variation of the spectral entropy (SE) and C0 complexity when the system takes different initial values. Also, in this paper, the initial conditions under which the system is in a synchronized state are determined by initial values with higher complexity. The correctness of the theoretical analysis and numerical simulation is verified by circuit simulation and hardware experiments. Finally, the new system achieves synchronization control utilizing a designed adaptive backstepping controller, laying the foundation for its subsequent use in secure communications. • A new three-dimensional Jerk chaotic system with line equilibrium points is constructed. • The new 3D jerk system has eight types of coexisting attractors and four types of extreme multistability. • The proposed system has six types of transient chaotic behavior. • Adaptive backstepping synchronization avoids the pain and complexity of designing multiple controllers. • Adaptive backstepping synchronization enables synchronization control when system parameters are unknown. [ABSTRACT FROM AUTHOR]

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. • A new berths and quay cranes allocation optimization model is modeled to satisfy the distribution plan. • This paper applies chaos mapping and quantum theory to improve the nonlinear convergence factor. • This paper designs the solution process of the whale feasible integer algorithm based on the chaotic and quantum theory. [ABSTRACT FROM AUTHOR]

This study explores the intrinsic characteristics of the (2+1)-dimensional Schwarz-Korteweg-de Vries equation used to describe shallow water waves. The multiple solitons are successfully constructed using a technique involving multiple exponential functions. Graphical representations of the results are provided in 3D, 2D, and density plots to assess the compatibility of the solutions. Also, the dynamic nature of studied equation is examined based on bifurcation and chaos theory for nonlinear systems. Bifurcation signifies how our dynamical system is affected by physical parameters in planar dynamical system. After that, we apply the external force on planar dynamical system to show the chaotic like behavior of the studied model. Such behavior is confirmed by utilizing different chaos detecting tools. The obtained results serve to explain the effectiveness and applicability of the utilized methodologies in comprehend the exact solution and qualitative behavior of nonlinear physical models. [ABSTRACT FROM AUTHOR]

Nonlinear kinetic energy harvesters are becoming more and more popular as well as advanced and efficient. This paper presents the study of the dynamics of such a system in a wide range of excitation parameters, assuming at the same time the possibility of a cyclical and smooth change of the potential function. We have designed a system that allows to obtain a wide spectrum of potential characteristics, from a single well to a three-well system, and we have analyzed its effectiveness. Next, we checked the influence of parameters characterizing the change of potential using bifurcation diagrams and their comparison with the effective voltage values. We also analyzed the behavior of the system in chaotic and periodic motion zones and presented selected sections of Poincare and Fourier amplitude-frequency spectra of chaotic solutions. The last element of the analysis was the impact of cyclic potential change on coexisting solutions. We have shown that the best effectiveness is achieved when the frequency of the external load is equal to the resonant frequency of the flexible cantilever beam and the change of potential is limited to extreme positions. • A new way of the potential function dynamic change in EH was proposed. • EH effectiveness analysis was made for chaotic and periodic motion zones. • Influence of the range and frequency of potential changes on the dynamics of the system was checked. [ABSTRACT FROM AUTHOR]

• Chaos theory is used to eliminate differences in the feature distribution of images with different modalities. • We propose a structure-aware feature extraction method to retain more features at the detail layer. • In this paper, proportional integral differential (PID) control is introduced into the fusion process. • Fusion experiments and object detection experiments demonstrate the superiority of our method. Differences in the imaging mechanisms of infrared and visible light images lead to differences in the way their visually meaningful gradients are formed. Existing fusion methods use the same feature extractor to extract features from the source video frames, which ignores the differences in the gradients of video frames from different modalities. In this paper, we propose an infrared and visible light video fusion method based on chaos theory and proportional integral differential (PID) control. Firstly, for the Lorentz chaotic system, we give it initial values and parameters, and iterate it to obtain three scrambling sequences, through which the source video frames are scrambled in the rows, columns, and diagonal directions respectively to eliminate their visually meaningful gradients, so that the features extracted are of comparable scales in the same layer, and the fusion process can be carried out in the scale-consistent space. Second, we propose a structure-aware relative total variation feature extraction method (saRTV) for the two-scale decomposition of source video frames, which can transfer more features of source video frames to the detail layer. Then, based on our previous work, this paper introduces PID control to construct a closed-loop control system through transfer function design, controller design and measurement function design. This control system is used to fuse the detail layer, so as to realize the real-time guidance of the source video frames to the fusion process. Experiments on public datasets demonstrate that our method has better performance compared to some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Memory resistor, or memristor, has been realized as a discrete electronic device and has a perspective application in the field of cryptography. The physical implementation of the memristor in chaotic circuits has been scarcely explored. In this paper, a memristor is fabricated by spin-coating a cobalt ferrite precursor on a processed silicon and is then electro-sputtered with silver to act as the anode with the base silicon as the cathode. This fabrication process has a scalability potential in conjunction with integrated circuit fabrication techniques and complementary metal oxide semiconductor (CMOS) technologies. The fabricated cobalt ferrite memristor has shown a ratio between the on and off resistance of >1000 and has been implemented in a chaotic Chua's circuit, making it one of few physical implementations of a physical memristor in a physical circuit. The analysis and characterization of this circuit using bifurcation diagrams and Lyapunov exponent prove the chaotic behavior of a real Chua's circuit. This chaotic behavior can be useful in chaotic cryptography as nonperiodic oscillations can be leveraged to make sensitive information more difficult to interpret by bad actors. [Display omitted] • A memristor is constructed on silicon to make fabrication process more scalable. • The memristor consists of spin-coated cobalt ferrite layer with active electrodes. • The memristor is implemented in Chua's circuit that exhibits chaotic behavior. • Chaotic behavior is proven with bifurcation and Lyapunov exponent analysis. [ABSTRACT FROM AUTHOR]

The accurate prediction of digging load serves as a fundamental cornerstone for advancing the development of intelligent and unmanned excavators. Given the complex nonlinear dynamics of digging load, this paper proposes a novel prediction model for excavator load power based on the chaos theory and support vector regression (SVR). The presence of chaos in the dynamic digging load system is detected through phase space reconstruction. SVR is utilized for nonparametric modeling and prediction, with the reconstructed phase space capturing the essential characteristics of excavator load and serving as inputs for SVR. To optimize the hyperparameters, an improved particle swarm optimization (IPSO) algorithm is presented. Excavation experiments conducted under two typical load conditions demonstrate the superiority of the proposed chaos-based IPSO-SVR model in terms of prediction accuracy. This research lays a solid foundation for practical load prediction in industrial excavator settings. [ABSTRACT FROM AUTHOR]

• The dynamic model of axially moving piezoelectric rectangular thin plate in thermal-electric-mechanical field is established. • The coupling relationship between thermal-electric-mechanical field and elastic deformation of thin plate are considered. • The influence mechanism on the resonance amplitude under the effects of thermal, force, electric and damping coefficients are clarified. In this paper, the combination resonance of parametric-forced excitation characteristics for an axially moving rectangular piezoelectric plate under a thermal-electromechanical field is studied. Based on Kirchhoff-Love plate theory and Von Karman theory, the transverse vibration governing equations are derived from Hamilton's principle. The equations are discretized to ordinary differential equations by the Galerkin method. Then, the multiple scales method is applied to solve the system combination resonance equation, two different resonance states and corresponding amplitude-frequency response equations are obtained by eliminating the secular term, respectively. Additionally, the stability of the steady-state responses is analyzed by Lyapunov stability. Based on the numerical analysis, the influence of axial velocity, external voltage, central temperature difference, structural damping, and other parameters on nonlinear combination resonance response are investigated. The effect of parameter variation on period-doubling bifurcation and the chaotic motion of the system are also discussed by the system global bifurcation diagram. [ABSTRACT FROM AUTHOR]

This study aims to investigate the significant dynamics of a Single Link Flexible Joint (SLFJ) Robotic Manipulator and implement chaotic control using the Adaptive Sliding Mode Control (ASMC) algorithm. The mathematical model of the system incorporates stiffness nonlinearity by introducing the function (x-x3) Various dynamical tools such as stability analysis of equilibrium points, sensitivity to initial conditions, orbit diagrams for parameter variations, Lyapunov spectrum, and frequency spectrum analysis are employed. The ASMC algorithm is utilized to suppress the chaotic behavior of the system. The equilibrium points are determined for critical parameter values, with the Jacobian matrix and corresponding eigenvalues exhibiting conjugate complex with negative real parts, indicating stability resembling a spiral saddle. Phase portraits illustrate the location and range of the chaotic attractor. Investigation of parameter ′ a ′ using orbit diagrams and Lyapunov spectrum reveals the transition from periodic to chaotic oscillations. The frequency spectrum confirms the chaotic nature of the system. Parameter estimation, state trajectories, and sliding surface analysis demonstrate that the ASMC scheme can effectively control the system in less than 0.3 s. Nonlinear stiffness has not been previously considered in SLFJ Robotic Manipulators, highlighting a novel aspect of this study. The results unveil new chaotic ranges for parameter variation previously undocumented. Frequency spectrum analysis is employed to distinguish between noise and chaotic oscillations, addressing a significant challenge in real-time systems. The ASMC algorithm is specifically designed to control chaotic oscillations, demonstrating its effectiveness in this context. • Novel Analysis: The research presents a comprehensive analysis of a Single Link Flexible Joint (SLFJ) Robotic Manipulator with nonlinear stiffness, shedding light on its intricate behavior and the impact of nonlinear dynamics. • Advanced Control Strategies: Through stability, bifurcation, and synchronization analyses, the study underscores the need for sophisticated control strategies, highlighting the effectiveness of the Adaptive Sliding Mode Controller (ASM) in achieving synchronization and stabilizing the system. • Practical Implications: By demonstrating the significance of nonlinear stiffness on system behavior and the efficacy of the ASM Controller in real-time applications, the research contributes valuable insights for enhancing the performance and reliability of robotic manipulator systems in practical scenarios. [ABSTRACT FROM AUTHOR]

Synchronization of satellite systems offers numerous advantages, including cost-effectiveness, flexibility, and extended area coverage. However, the presence of chaotic behavior in such systems poses substantial challenges. This paper investigates chaos in satellite systems and proposes a novel approach - the Novel Integral Terminal Sliding Mode (NITSM) controller - specifically designed for synchronizing the angular velocities of chaotic Leader-Follower satellite systems. The NITSM controller leverages limited-time features to eliminate chattering and exhibits remarkable robustness against external disturbances such as cosmic rays and solar storms. MATLAB simulations are conducted to validate the effectiveness of the proposed method, comparing the synchronization error of the NITSM controller with a common approach. The results demonstrate the superior performance of the Novel Integral Terminal Sliding Mode controller, showcasing reduced response time, robust behavior, and a substantial six-fold reduction in angular velocity synchronization error. [ABSTRACT FROM AUTHOR]

Artificial Intelligence is extensively applied in heartcare to analyze patient data, detect anomalies, and provide personalized treatment recommendations, ultimately improving diagnosis and patient outcomes. In a field where accountability is indispensable, the prime reason why medical practitioners are still reluctant to utilize AI models, is the reliability of these models. However, explainable AI (XAI) was a game changing discovery where the so-called back boxes can be interpreted using Explainability algorithms. The proposed conceptual model reviews the existing recent researches for AI in heartcare that have found success in the past few years. The various techniques explored range from clinical history analysis, medical imaging to the nonlinear dynamic theory of chaos to metabolomics with specific focus on machine learning, deep learning and Explainability. The model also comprehensively surveys the different modalities of datasets used in heart disease prediction focusing on how results differ based on the different datasets along with the publicly available datasets for experimentation. The review will be an eye opener for medical researchers to quickly identify the current progress and to identify the most reliable data and AI algorithm that is appropriate for a particular technology for heartcare along with the Explainability algorithm suitable for the specific task. [ABSTRACT FROM AUTHOR]

As a data-centric network, the Mobile Crowd Sensing (MCS) collects and uploads sensing data through intelligent terminal devices carried by workers. However, due to resource limitations, the confidentiality, integrity and communication cost issues of sensing data have not been well coordinated and resolved in the actual MCS data collection process. In this regard, this paper proposes an edge computing-assisted MCS Chaotic Compressed Sensing Secure Data Collection scheme (CCS-SDC), which supports the secure collection of sensing data and saves communication cost. In CCS-SDC, workers first use the encryption algorithm based on chaos theory to encrypt the collected sensing data, and then adopt the hash location algorithm based on chaos theory to calculate the corresponding hash verification code of the sensing data. After receiving the encrypted sensing data transmitted by the worker, the edge server recomputes the hash verification code of the encrypted sensing data and verifies the integrity of the data, which can locate the changed sensing task data to a certain extent. Then the sensing data is compressed and sampled based on the generated chaos measurement matrix to reduce the amount of data transmission and further enhance the confidentiality of the sensing data. In addition, the same hash positioning algorithm is used between the edge server and the sensing platform to protect data integrity. For the changed data located by integrity verification, in addition to choosing to let workers re-sense and submit, the sensing platform can also choose to discard the changed sensing data under appropriate circumstances, and still reconstruct and decrypt the remaining data through the proposed algorithm to obtain effective original sensing data. The experimental evaluation results on real data sets show that CCS-SDC achieves the best effects, not only achieving lower sensing data communication cost than other related schemes, but also better protecting the confidentiality and integrity of sensing data, which is very useful for resource-constrained MCS data collection scenarios. [ABSTRACT FROM AUTHOR]

External disturbances are always inevitable in complex application scenarios, especially in synchronizing chaotic systems. This paper proposes a noise-restraint zeroing neural network (NRZNN) model to expedite the synchronisation of chaotic systems under external disturbances. Its associative controller is then evolved to suppress the interference of external noise. Theoretical analysis shows that the NRZNN model and its associated controller have inherent robustness. For comparison, the conventional zeroing neural network (CZNN) approach is utilized for the synchronisation of chaotic systems. Numerical comparison results validate the efficiency of the NRZNN model for synchronising chaotic systems under the constant noise disturbance. Moreover, through additional tests, it is found that the proposed NRZNN model can also suppress time-dependent noise during the synchronization of chaotic systems. Finally, the effect on the convergence performance is further investigated by adjusting the values of design parameters. [ABSTRACT FROM AUTHOR]

This paper deals with the sliding mode stabilization for chaotic systems. In the system under consideration, the nonlinear function is one-sided Lipschitz with quadratic inner-boundedness. Specifically, a non-fragile sliding mode surface is constructed, and the sufficient condition for the convergence is derived. Then, a new feedback law is proposed to enable the state trajectories of the closed-loop system to reach the sliding mode surface in finite time. Finally, an example in the background of the unified chaos system is simulated to show the validation of the designed controller. [ABSTRACT FROM AUTHOR]

The existence and identification of chaos regarding in-plane pitch motions of tethered satellite systems are scientific problems of concern, and are directly related to normal system operations in the station-keeping phase. This paper studies the effect of microamplitude longitudinal oscillation on the occurrence of chaos in a tethered system subjected to atmospheric perturbations. Based on a simplified rod model that considers tether elasticity and satellite masses, the Melnikov method is used to identify a criterion that can predict chaos, and a chaotic zone is further proposed to recognize the relationship between the chaos and system parameters. Then the cell mapping method is used to describe the system's global dynamic behaviors, including chaos. A discrete model of the flexible system that consists of particles connected by massless springs and satellite rigid bodies is structured so that more accurate dynamic simulations can be used to verify the theoretical analysis. Finally, numerical examples demonstrate that the chaotic zone and criterion expression are useful tools for revealing chaos. The relationship between the dynamics and system parameters is also assessed. The results of the simplified model agree with those of the sophisticated model. • A chaotic criterion and a chaotic zone on a tethered satellite system are proposed. • The relationship between the dynamics and system parameters is estimated. • The global dynamic characteristics of the system are revealed via cell mapping. [ABSTRACT FROM AUTHOR]

• Traditional epidemiological models may struggle to accurately capture the chaotic nature of a pandemic/epidemic. • Chaos theory applied to epidemiology can capture and help to invistigate the non-linear dynamics underlying the progression of COVID-19 and other pandemics/epidemics. • Chaos theory can assist in analyzing complex interactions that can either exacerbate or mitigate the spread of a pathogen circulating in the human population. • Chaos theory might give information on the chances for an emerging virus to establish a long-lasting relationship with a new host. • Insights from chaos theory underscore the importance of flexibility and adaptability in response strategies. The chaos theory, a field of study in mathematics and physics, offers a unique lens through which to understand the dynamics of the COVID-19 pandemic. This theory, which deals with complex systems whose behavior is highly sensitive to initial conditions, can provide insights into the unpredictable and seemingly random nature of the pandemic's spread. In this review, we will discuss some literature data with the aim of showing how chaos theory could provide valuable perspectives in understanding the complex and dynamic nature of the COVID-19 pandemic. In particular, we will emphasize how the chaos theory can help in dissecting the unpredictable, non– linear progression of the disease, the importance of initial conditions, and the complex interactions between various factors influencing its spread. These insights are crucial for developing effective strategies to manage and mitigate the impact of the pandemic. [ABSTRACT FROM AUTHOR]

We theoretically investigate on the evolution of spatiotemporal chaos under the influence of Raman gain, in an optical ring microresonator. The dynamics of the system is shown to be governed by the Lugiator–Lefever equation, with an additional real and imaginary Raman gain term. In the absence of pump field intensity and Raman gain, we observe an increase in the amplitude and frequency of the traveling optical field as the pump detuning frequency increases. However this field gradually vanishes as time increases, owing to the intra-cavity loss. By exploring an appropriate ansatz which incorporate a chirping parameter, the modified Lugiator–Lefever equation is transformed to a set of four coupled first-order nonlinear ordinary differential equations. Fixed point stability analysis strongly suggest that variation in Raman gain has the propensity of inducing the co-existence of bright and dark solitons in the anomalous dispersion regime. Results of numerical simulations underscore that the structural profiles of the optical field amplitude are greatly modified by the Raman effects. Variation in Raman gain equally leads to a bifurcation analysis of the system, in which the Lyapunov exponent diagrams reveal regions of period doubling and chaos. We finally observe that for a fixed value of the real part of Raman gain coefficient, an increase in the effects of soliton self-frequency shift generally drives the system to chaotic regime. • Evolution of spatiotemporal chaos under the influence of Raman gain, in ring microresonator. • Variation in Raman gain induces the co-existence of bright and dark solitons in the anomalous dispersion regime. • The Lyapunov exponent diagrams reveal regions of period doubling and chaos. • An increase in the effects of SSFS generally drives the system to chaos, for fixed value of the real part of Raman gain coefficient. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. The I t o ˆ -stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. Subsequently, the stochastic stability and bifurcation behaviors of the system are analyzed. Furthermore, using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D -bifurcation and stochastic P -bifurcation. We also analyze the properties and shape changes of the system's probability density function under different parameters through numerical simulation. It has been determined that the system exhibits stochastic bifurcation behavior, specifically P -bifurcation and D -bifurcation. The validity of the method is verified by a numerical model. The theoretical chaos threshold of the system is determined using the random Melnikov method, and the impact of delayed feedback parameters on the chaotic motion of the system is analyzed by combining the bifurcation diagram, phase portrait, and time series. • We investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. • The Ito-stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. • Using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D-bifurcation and stochastic P-bifurcation. • The theoretical chaos threshold is determined using the random Melnikov method. [ABSTRACT FROM AUTHOR]

This paper considers system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We analyze an optimization objective derived from Bayesian inference for the dynamics of hidden Markov models. We then relate this objective to that used in several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that the proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics' origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach identifies accurate and generalizable models even when there are more parameters than data or when the system exhibits chaotic behavior. • Modeling of model uncertainty with process noise leads to inherent regularization. • Process noise induces objective function smoothness similarly to multiple shooting. • Certain Markov parameter estimation methods treat data as conditionally independent. • Bayesian system ID outperforms state-of-the-art methods on small, noisy datasets. [ABSTRACT FROM AUTHOR]

• Analysis of a seasonal plankton model with added mixotroph population. • Demonstrate potential for chaos in year-to year mixotroph density with enrichment. • Prediction of mixo-HABs may not be possible using environmental predictors alone. Mixotrophic nutrition, in which organisms combine aspects of heterotrophic and autotrophic nutrition, is a common characteristic amongst the phytoplankton, and especially amongst harmful algae bloom (HAB) species. To explore how the addition of a mixotrophic population influences a theoretical plankton system under different enrichment levels, we employ a previously published numerical plankton model that reproduces seasonal succession dynamics. Through this work we found potential for chaos to occur as the system was enriched. Focusing on occurrence of chaos in the mixotroph population, a novel finding, we conducted a bifurcation analysis which demonstrated a period doubling route to chaos. Further, we demonstrate that the occurrence of chaotic dynamics in the model system is not an artifact of the mixotroph life-history trait values used in our initial simulations, rather chaos was found to occur under a wide range of mixotroph trait value combinations. Through our trait analysis, we also found that regardless of whether or not the system was chaotic for a specific combination of values, variation in the mixotroph population peak population density could be high between consecutive years. These findings have implications that are important for the management of nutrients in aquatic systems and HABs. Results shed light on why it may be difficult to predict the occurrence of mixotrophic HABs based solely on environmental variables, when the year-to-year peak density of the mixotroph is chaotic or highly variable with enrichment. These results also demonstrate how initiation of a mixotrophic HAB might occur with enrichment, due to erratic population spikes, when broadcast allelopathic or toxic chemicals are at low concentrations, a novel bloom initiation mechanism. [ABSTRACT FROM AUTHOR]

Images play a vital role in almost all sectors, including medical, video conferencing, weather forecasting, military applications, and most common social media applications. Today's proliferating technology provides attackers an opportunity to breach and access confidential data that are not enciphered or weakly secured. There is a massive requirement for a robust image cryptosystem for the secure transmission of confidential images over an insecure network. Here, we present an encryption technique to encipher images using dynamic substitution boxes (S-boxes) generated by a chaotic system and the points from an elliptic curve over a finite field. The dynamic S-boxes generation depends on a key obtained from the hash value using Secure Hash Algorithm-512 (S H A 512). Each different image generates different S-boxes making it immune to known-plaintext attacks. The input image pixels are permuted and substituted using dynamic permutation tables and dynamics S-boxes. The mean of S-box security analyses such as non-linearity, strict avalanche criterion, bit independent criterion, differential approximation probability, and linear approximation is obtained as 104, 0.510294, 0.51145, 0.046875, and 0.083252 respectively. The generated S-boxes using the proposed method meet the standards of secure S-boxes. The cipher output images produced by the proposed methodology are also examined using statistical and security analyses. The proposed method can resist cipher-text-only attacks and has a large keyspace of 512 bits to withstand a probabilistic or deterministic attack on the elliptic curve discrete logarithmic problems such as baby-step, giant-step attack, and Pollard's rho attack. The strength of the generated cipher image using the proposed method is substantiated by tests such as the National Institute of Standards and Technology randomness test, the local entropy, correlation analysis, and differential analysis. Comparisons are made with some of the related existing state-of-the-art methods and turn out to be on par or better with the other compared methods. [ABSTRACT FROM AUTHOR]