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Nowadays, establishing security in data transmission is essential, and it is achieved by cryptography. Encryption of still or video images in specific applications such as Internet of Things, medical and satellite imaging, in applications requiring high-speed encryption, or even in applications where a personal computer is unavailable or cannot be used needs special hardware. In this paper, an image encryption algorithm based on chaos theory named Parallel Chaotic Checksum-based Image Encryption or PCCIE algorithm is proposed that has been able to provide a fast, efficient and secure algorithm with a hardware perspective on the design and parallel system structure. Using high-level synthesis, PCCIE is implemented on a Field Programmable Gate Array (FPGA). The proposed algorithm using small and independent local image buffers solved FPGA internal memory limitation for encryption of large images. Ultimately, a Hexa-core crypto-processor with single-precision floating-point and fixed-point precision has been designed, capable of encrypting 256 × 256 and Full HD images in 2.13 and 59.52 milliseconds, respectively, at 469 and 16 frames per second. [ABSTRACT FROM AUTHOR]

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields. [ABSTRACT FROM AUTHOR]

In order to solve the dynamic analysis and chaotic motion control problems of the current-mode-controlled Boost converter system, a state equation model in the continuous current mode is established. The evolutionary path of the periodic motion of the system through the doubling bifurcation to the chaotic motion is analyzed by the bifurcation diagram, Poincaré sections and phase portraits. Then, according to the fundamental principle of the resonant parametric perturbation (RPP) method, a controller is designed based on the model-free adaptive control (MFAC) method to output the perturbation amplitude, and the disturbance quantity is calculated according to the perturbation amplitude. By adding a small amplitude disturbance to the controllable parameter of the controlled system, the chaotic motion of the system is guided to expected periodic orbit. The advantage of this method is that no precise mathematical model (PMM) of the system is required. At the same time, the design of the controller is simple and easy to implement. [ABSTRACT FROM AUTHOR]

This article is a tribute to Oleksandr Mykolayovych Sharkovsky, a renowned mathematician and one of the founders of the mathematical concept of deterministic chaos. Sharkovsky's groundbreaking work, including his famous Sharkovsky theorem, has had a significant impact on the theory of dynamical systems. The article highlights Sharkovsky's early life, education, and career, as well as his contributions to the field of mathematics. It also mentions his achievements, such as publishing 10 monographs and over 250 research works, and receiving several prestigious awards. Sharkovsky's work continues to be influential in the study of nonlinear dynamics and chaos theory. [Extracted from the article]

Smartphones, digital cameras, and other imaging devices generate vast amounts of high-resolution colored images daily, stored on devices equipped with multi-core central processing units or on the cloud. Safeguarding these images from potential attackers has become a pressing concern. This paper introduces a set of six innovative image ciphers designed to be stronger, faster, and more efficient. Three of these algorithms incorporate the State-Based Tent Map (SBTM) Chaotic Pseudo Random Number Generator (CPRNG), while the remaining three employ a proposed modified variant, SBTMPi. The Grayscale Image Cipher (GIC), Colored Image Cipher Single-Thread RGB (CIC1), and Colored Image Cipher Three-Thread RGB (CIC3) showcase the application of the proposed algorithms. By incorporating novel techniques in the confusion and diffusion phases, these ciphers demonstrate remarkable performance, particularly with large colored images. The study underscores the potential of SBTM-based image ciphers, contributing to the advancement of secure image encryption techniques with robust random number generation capabilities. [ABSTRACT FROM AUTHOR]

The security and integrity of medical data, in particular, have become significant concerns due to the substantial expansion in the healthcare environment due to the internet of things (IoT). To guarantee data security during transmission, this research suggests a chaotic healthcare monitoring system. This system employs a new 5- dimension (5D) chaotic system in conjunction with the secure hash algorithm version three (SHA3-256), salsa 20, and deoxyribonucleic acid (DNA). Lyapunov's proposed 5D chaos system was tested and passed for several initial periods, yielding a super chaos system (3 positive Lyapunov). Salsa 20 and randomly generated chaotic keys were utilized for encryption and decryption operations. The method we created will assess a patient's body temperature, heart rate, and oxygen saturation levels in the blood and communicate the data to a healthcare center through the Message Queuing Telemetry Transport (MQTT) protocol. The suggested system ensures that patient data is transmitted via the internet or an intranet in a secure, reliable, and readily accessible manner. In several studies involving security analysis, The encryption time is 1.872, the throughput (in bits per second (bps)) is 273.2642, and the memory usage (in megabytes) is 10.6211. The performance analysis confirmed the proposed cryptosystem's capacity to withstand multiple attacks due to its low computational and communication costs and broad key space. [ABSTRACT FROM AUTHOR]

Due to the potential security problem of the key management and distribution for the symmetric image encryption schemes, this paper proposes a new asymmetric image encryption method based on a singular cubic curve and chaos theory. The Diffie-Hellman algorithm is used to generate the initial values of a chaotic map by exchanging public keys. The image encryption process is carried out using a chaotic map, in which a random sequence of the same length as the image to be encrypted is generated using the standard map, and then bitwise XOR is used to create confusion in the image's pixels. Also, an Arnold cat map is used to change the location of pixels and diffusion in them is obtained. Gray images with size 256×256 are used in this algorithm. The simulation results and security analysis indicate that the scheme can withstand common attacks such as statistical attacks, differential attacks, and other attacks. [ABSTRACT FROM AUTHOR]

The short-term traffic flow prediction can help to reduce flight delays and optimize resource allocation. Using chaos dynamics theory to analyze the chaotic characteristics of en-route traffic flow is the basis of short-term en-route traffic flow prediction and ensuring the orderly and smooth state of the en-route. This paper takes the time series of en-route traffic flow extracted from Automatic-Dependent Surveillance Broadcast (ADS-B) measured data as the research object, uses the improved C–C method to reconstruct the phase space, and uses the improved small data volume method to calculate the Lyapunov index to identify the chaos phenomenon of en-route traffic flow. In order to avoid the interference of chaos phenomenon on traffic prediction, the Wavelet Neural Network (WNN) model is established to predict the traffic flow at en-route points. The experimental shows that when the number of iterations is 10,000, the average accuracy of WNN prediction is 0.87173, and the average running time is 6.9335334 s. According to the experimental results, it can be seen that the smaller number of iterations has more advantages in running time, which greatly reduces the overall running time. At the same time, it indicates that appropriately increasing or reducing the number of iterations in this experiment has little effect on the results. [ABSTRACT FROM AUTHOR]

Memristors have several chaotic dynamic models and have been used successfully in various fields, including secure communication systems, information storage, and artificial neural networks. The memristor-based four-dimensional chaotic (FDMC) systems generate unpredictable and intricate time domain signals. Parameter fluctuations in the FDMC system may give birth to chaos, making it difficult to suppress. Stabilizing chaos in the FDMC system improves the circuit's performance. This paper synthesizes a novel time-efficient chatter-free nonlinear robust adaptive control (NLRAC) technique that stabilizes chaos in the FDMC system affected by time-varying unknown bounded exogenous disturbances and model uncertainties. The proposed NLRAC strategy decimates the time-varying unknown bounded exogenous disturbances and model uncertainties effects; it establishes a faster, smoother state-variable trajectories convergence to the zero vicinity. The theoretical analysis and mathematical proofs are based on the Lyapunov stability technique. Computer simulation results show that the proposed NLRAC technique effectively brings the FDMC system's state-variable trajectories to zero with reduced fluctuations for control input signals and state-variable trajectories. This feedback controller's attribute enhances closed-loop stability performance, improves precision, and reduces risk overshoot. The paper includes comparative computer simulation results to endorse the proposed controller performance. [ABSTRACT FROM AUTHOR]

Nonlinear dynamical problems, characterized by unpredictable and chaotic changes among variables over time, pose unique challenges in understanding. This paper explores the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation-a fundamental equation in applied magnetism and nanophysics. The study focuses on dynamic behaviors, specifically examining bifurcations and equilibrium points leading to chaotic phenomena by introducing an external term to the system. Employing chaos theory, we showcase the chaotic tendencies of the perturbed dynamical system. Additionally, a sensitivity analysis using the Runge-Kutta method reveals the solution's stability under slight variations in initial conditions. Innovatively, the paper utilizes the planar dynamical system technique to construct various solitons within the governing model. This research provides novel insights into the behavior of the (2+1)-dimensional cmKdV equation and its applications in applied magnetism and nanophysics. [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]

DC microgrids have emerged as a promising solution to provide reliable and efficient power for various applications. However, similar to any power system, DC microgrids are prone to faults that can disrupt their performance. Accordingly, the lack of publication of sufficient standards and guidelines for the protection of DC microgrids makes it necessary to develop protection methods in these networks. Therefore, the purpose of this paper is to create a new fault detection method in islanded DC microgrids. In this method, the current signal samples are entered into a chaotic state, and using the feature of sensitivity to the initial conditions of this method, it accurately identifies the fault. In this case, the signal undergoes a very large chang during the fault, which is easily visible compared to the normal state. It should be noted that, unlike other methods, in the proposed method in this paper, only one measurement unit is used in the DC bus for sampling signals. Therefore, there is no need to use communication links in the proposed method. The proposed method has been implemented using MATLAB/Simulink software on a sample DC microgrid. The results show that the proposed method is capable to detect pole-to-pole and pole-to-ground faults on the microgrids and also faults on the distributed generations and electrical vehicles. Also, results prove that this method is resistant to the operational uncertainty of distributed generations, electrical vehicles, and the destructive effects of noise on the sampled signals. [ABSTRACT FROM AUTHOR]

This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have established the occurrence of various types of bifurcations, including flip bifurcation and Neimark-Sacker bifurcation. Furthermore, to address the observed chaotic behavior in the system, three controllers were designed by employing state feedback control, OGY feedback control, and hybrid control methods. These controllers serve to control chaos in the proposed system and identify specific conditions under which chaos or bifurcations can be stabilized. Finally, the theoretical analyses have been validated through numerical simulations. [ABSTRACT FROM AUTHOR]

This study draws on the parallelism between digitalization and the complexity of the Islamic banking industry (IBs) in a postpandemic era. It examines the digital Butterfly Effect on the Islamic banking industry to promote tech-driven IBs through an empirical lens. The study constructs a Fintech adoption index (FADi) and uses a Bayesian vector Auto-Regressive model, causality tests and impulse response functions for yearly data from 2008 to 2022 to examine the possible magnified effect of adopting Fintech by the Islamic banking industry in Malaysia. Key findings suggest that embracing Fintech by the IBs enhances the profitability of the banks, which is measured by the return on asset and return on equity. In addition, the study reports a ripple effect of FADi on the broader spectrum of the Malaysian economy. This indicates that Fintech fosters economic growth, household consumption, financial and insurance services, and corporate taxes. On the other hand, Fintech adoption helps reduce the unemployment rate. The findings contribute to the literature by investigating the IB as a system within financial chaos theory and the possible Butterfly Effect triggered by Fintech adoption. [ABSTRACT FROM AUTHOR]

Metaheuristic techniques are capable of representing optimization frames with their specific theories as well as objective functions owing to their being adjustable and effective in various applications. Through the optimization of deep learning models, metaheuristic algorithms inspired by nature, imitating the behavior of living and non-living beings, have been used for about four decades to solve challenging, complex, and chaotic problems. These algorithms can be categorized as evolution-based, swarm-based, nature-based, human-based, hybrid, or chaos-based. Chaos theory, as a useful approach to understanding neural network optimization, has the basic idea of viewing the neural network optimization as a dynamical system in which the equation schemes are utilized from the space pertaining to learnable parameters, namely optimization trajectory, to itself, which enables the description of the evolution of the system by understanding the training behavior, which is to say the number of iterations over time. The examination of the recent studies reveals the importance of chaos theory, which is sensitive to initial conditions with randomness and dynamical properties that are principally emerging on the complex multimodal landscape. Chaotic optimization, in this regard, accelerates the speed of the algorithm while also enhancing the variety of movement patterns. The significance of hybrid algorithms developed through their applications in different domains concerning real-world phenomena and well-known benchmark problems in the literature is also evident. Metaheuristic optimization algorithms have also been applied to deep learning or deep neural networks (DNNs), a branch of machine learning. In this respect, the basic features of deep learning and DNNs and the extensive use of metaheuristic algorithms are overviewed and explained. Accordingly, the current review aims at providing new insights into the studies that deal with metaheuristic algorithms, hybrid-based metaheuristics, chaos-based metaheuristics as well as deep learning besides presenting recent information on the development of the essence of this branch of science with emerging opportunities, applicability-based optimization aspects and generation of well-informed decisions. [ABSTRACT FROM AUTHOR]

We explore the transition to chaos in a prototypical hydrodynamic oscillator, namely a globally unstable low-density jet subjected to external time-periodic forcing. As the forcing strengthens at an off-resonant frequency, we find that the jet exhibits a sequence of nonlinear states: period-1 limit cycle $\rightarrow $ quasiperiodicity $\rightarrow$ intermittency $\rightarrow$ low-dimensional chaos. We show that the intermittency obeys type-II Pomeau–Manneville dynamics by analysing the first return map and the scaling properties of the quasiperiodic lifetimes between successive chaotic epochs. By providing experimental evidence of the type-II intermittency route to chaos in a globally unstable jet, this study reinforces the idea that strange attractors emerge via universal mechanisms in open self-excited flows, facilitating the development of instability control strategies based on chaos theory. [ABSTRACT FROM AUTHOR]

To research the special transmission system type of the multistage closed-loop gear system of the 3D braiding machine, a multi-degree of freedom nonlinear dynamic model was established by using the lumped mass method, taking into account parameters such as meshing stiffness, static transmission error, backlash, and meshing damping. To reduce the computational complexity, a gear system with 12 gears was selected and solved using the Runge-Kutta method. Using meshing frequency, backlash, and meshing damping ratio as control parameters, we analyzed the bifurcation and chaos of the system under different conditions through bifurcation diagrams. Simultaneously using sequence diagram, phase plane diagrams, Poincare maps, and FFT diagrams to accurately display the motion state of the system. The analysis results indicate that with the increase of meshing frequency and backlash, the system exhibits a range of motion states, such as period-one motion, multi-periodic motion, quasi-periodic motion, and chaotic motion. Meanwhile, increasing the damping ratio can effectively suppress the chaotic state of the gear system and also reduce the maximum vibration displacement of the gear system. [ABSTRACT FROM AUTHOR]

In recent times, there have been notable advancements in solar energy and other renewable sources, underscoring their vital contribution to environmental conservation. Solar cells play a crucial role in converting sunlight into electricity, providing a sustainable energy alternative. Despite their significance, effectively optimizing photovoltaic system parameters remains a challenge. To tackle this issue, this study introduces a new optimization approach based on the coati optimization algorithm (COA), which integrates opposition-based learning and chaos theory. Unlike existing methods, the COA aims to maximize power output by integrating solar system parameters efficiently. This strategy represents a significant improvement over traditional algorithms, as evidenced by experimental findings demonstrating improved parameter setting accuracy and a substantial increase in the Friedman rating. As global energy demand continues to rise due to industrial expansion and population growth, the importance of sustainable energy sources becomes increasingly evident. Solar energy, characterized by its renewable nature, presents a promising solution to combat environmental pollution and lessen dependence on fossil fuels. This research emphasizes the critical role of COA-based optimization in advancing solar energy utilization and underscores the necessity for ongoing development in this field. [ABSTRACT FROM AUTHOR]

Chaotic systems depict complex dynamics, thanks to their nonlinear behaviors. With recent studies on fractional-order nonlinear systems, it is deduced that fractional-order analysis of a chaotic system enriches its dynamic behavior. Therefore, the investigation of the chaotic behavior of a 4D memristive Chen system is aimed in this study by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Based on these analyses, two different fractional orders (i.e., q = 0.948 and q = 0.97) are determined where the 4D memristive system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the fractional-order memristive chaotic system on the equilibrium points. Then, control method results are obtained by both numerical simulations and different illustrative experiments of microcontroller-based realization. As expected, voltage outputs of the microcontroller-based realization are in good agreement with the time series of numerical simulations. [ABSTRACT FROM AUTHOR]

With the rapid development of computer network technology, it is often necessary to collect weak signals to collect favorable information. The development of signal detection technology is ongoing; however, various issues arise during the detection process. These issues include low efficiency and a high signal noise threshold. However, many problems will be encountered in the process of detection. In order to solve these problems, the nonlinear chaos theory is introduced to detect signals, and the simulation experiments of weak pulse signals and weak partial discharge signals are carried out respectively. The experimental results showed that the detection effect was remarkable in the quasi periodic state, and it had a good detection effect for weak pulse signals. At a signal-to-noise ratio of - 25 dB, double coupling system, two-way ring coupling system, and single ring coupling system displayed detection success rates exceeding 98%. Meanwhile, the detection success rate of the strong coupling system was only 12%. Even at a noise signal ratio as low as - 40 dB, the dual coupling system still maintained a detection success rate above 80%. The simulation results of partial discharge signal detection showed that there was a high fluctuation only at 2 ms, and the rest was basically stable at about 0 V, indicating that the system had a strong suppression effect on Gaussian white noise. When comparing the simulation results of the detection of the new chaotic system and the double coupling system, it was found that the new chaotic system has a superior impact in detecting weakly attenuated partial discharge signals. Through analysis of the system's dynamic behavior, the research confirms its rich dynamic characteristics and sheds light on the reasons for phase state mutation and missed detection. The noise system is utilized for comparing the performance of various systems, with the goal of enhancing the system's detection capability. [ABSTRACT FROM AUTHOR]

Herringbone gear planetary gear transmission system has the advantages of high contact ratio and high bearing capacity and is widely used in various heavy load fields. However, the gear generates a large amount of heat during the meshing transmission, which affects the nonlinear dynamic characteristics of the system. In this paper, the various nonlinear factors are considered, including time-varying meshing stiffness, engagement damping, backlash, and engagement error. A nonlinear dynamic model of the herringbone planetary gear system considering temperature effects is established by using the lumped-parameter method. The nonlinear vibration differential equation of the system is solved by using the Runge–Kutta method. The impact law of temperature and engagement damping ratio changes on the bifurcation features of the herringbone planetary gear system is studied by combining the maximum Lyapunov exponent diagram, bifurcation diagram, time domain diagram, phase diagram, Poincare diagram, and spectrogram. And the chaos phenomenon of the system is analyzed and controlled by using a non-feedback control method with the external periodic signal. The result shows that with the change of temperature rise and meshing damping ratio, the system exhibits the kinematics response of chaotic, multi-period, and single-period. Higher temperature rise (∆T > 64 °C) and larger engagement damping ratio (ξ > 0.122) can make the gear system enter stable periodic motion. The chaotic motion region of the system is effectively controlled to the periodic motion orbit by introducing the periodic signal feedback controller. The relevant conclusions can provide a theoretical basis for the optimal design of the dynamic structure stability of herringbone planetary gear. [ABSTRACT FROM AUTHOR]

This paper proposes a new four-dimensional hyper-chaotic system capable of generating multi-wing chaotic attractors by introducing active magnetron memristors, multi-segmented square functions and trigonometric functions. The dynamical properties of this new hyper-chaotic system, such as equilibrium point, dissipation, Lyapunov exponential spectrum, bifurcation diagram and Poincaré cross-section and attraction basin, are analyzed theoretically and simulated numerically, and the complexity of this system with different parameters is analyzed. It is observed that this hyper-chaotic system has periodic, chaotic and hyper-chaotic variations with an infinite number of equilibria and coexisting attractors under different parameter conditions. The circuit simulation was performed using Multisim and the results obtained were consistent with the numerical analysis of the dynamics, and the chaotic circuit system is designed by FPGA to verify the realizability of the system. Finally, an image encryption algorithm is designed in conjunction with the DNA algorithm to enable a new system chaotic sequence for image encryption. The results show that the hyper-chaotic system has rich dynamical behavior and has high-security performance when applied to image encryption with strong chaotic key and plaintext sensitivity and large key space in image encryption. [ABSTRACT FROM AUTHOR]

Thunderstorms endanger life and infrastructure. The accurate and precise prediction of thunderstorms is therefore helpful to enable protection measures and to reduce the risks. This manuscript presents the latest developments to improve thunderstorm forecasting in the first few hours. This includes the description and discussion of a new Julia-based method (JuliaTSnow) for the temporal extrapolation of thunderstorms and the blending of this method with the numerical weather prediction model (NWP) ICON. The combination of ICON and JuliaTSnow attempts to overcome the limitations associated with the pure extrapolation of observations with atmospheric motion vectors (AMVs) and thus increase the prediction horizon. For the blending, the operational ICON-D2 is used, but also the experimental ICON-RUC, which is implemented with a faster data assimilation update cycle. The blended products are evaluated against lightning data. The critical success index (CSI) for the blended RUC product is higher for all forecast time steps. This is mainly due to the higher resolution of the AMVs (prediction hours 0–2) and the rapid update cycle of ICON-RUC (prediction hours 2–6). The results demonstrate the potential of the rapid update cycle to improve the short-term forecasts of thunderstorms. Moreover, the transition between AMV-driven nowcasting to NWP is much smoother in the blended RUC product, which points to the advantages of fast data assimilation for seamless predictions. The CSI is well above the critical value of 0.5 for the 0–2 h forecasts. Values below 0.5 mean that the number of hits (correct informations) is lower than the number of failures, which results from the missed cells plus false alarms. The product is then no longer useful in forecasting thunderstorms with a spatial accuracy of 0.3 degrees. Unfortunately, with RUC, the CSI also drops below 0.5 when the last forecast is more than 3 h away from the last data assimilation, indicating the lack of model physics to accurately predict thunderstorms. This lack is simply a result of chaos theory. Within this context, the role of NWP in comparison with artificial intelligence (AI) is discussed, and it is concluded that AI could replace physical short-term forecasts in the near future. [ABSTRACT FROM AUTHOR]

Modeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large subset of the multidimensional parameter space, the return map of the voltage dynamics is an expanding Lorenz map, we analyze both chaotic and periodic behavior of the system and describe the complexity of spiking patterns fired by a neuron. This is achieved by using and extending some results from the theory of Lorenz-like and expanding Lorenz mappings. [ABSTRACT FROM AUTHOR]

Aims Patients with heart failure (HF) can exhibit kinesiophobia, an excessive, debilitating, and irrational fear of movement. This study aimed to enhance the understanding of kinesiophobia in patients with HF by analysing associations with the following variables: musculoskeletal pain, quality of life, quality of sleep, functional capacity, disability, frailty, sex, and age. Methods and results In this cross-sectional study, 107 participants were included, with ages ranging from 28 to 97 years (57% men, mean age 73.18 ± 12.68 years). Multiple regression analyses were performed with all variables, including polynomial regressions for variables with a non-linear relationship. Kinesiophobia was significantly correlated (P < 0.01) with musculoskeletal pain, quality of life, quality of sleep, functional capacity, disability, and being at risk of frailty, while age and sex were not statistically significant. Frailty disability and musculoskeletal pain intensity were variables linearly associated with kinesiophobia, while quality of sleep and disability had a non-linear relationship with kinesiophobia. Conclusion Kinesiophobia needs to be evaluated and better understood in patients with HF to improve physical activity and exercise adherence. This study found that musculoskeletal pain intensity, quality of sleep, disability, and frailty risk have a significant association with kinesiophobia in patients with HF. Our results suggest multi-dimensional associations of kinesiophobia in patients with HF, which require further examination and understanding. [ABSTRACT FROM AUTHOR]

In the actual printing production process, the printing electronic motion membrane is susceptible to transverse vibration caused by interference from air drag, temperature changes, and other external conditions, resulting in membrane wrinkles, slippage, and other phenomena in the transmission process. We studied the bifurcation and chaos movement properties of anisotropic membranes under air drag and temperature. According to D'Alembert's theory and von Kármán's principle, the nonlinear dynamic differential formulas of axially moving anisotropic membranes with gas-thermal-elastic coupling are established. The Galerkin method is applied to discretize the formulas to obtain the state equation of the system. Finally, numerical simulations are performed by applying the fourth-order Runge–Kutta method to analyze the bifurcation and chaos of the system in terms of orthotropic coefficient, dimensionless air drags, and dimensionless temperature. The bifurcation diagrams, Lyapunov exponent diagrams, displacement time-history diagrams, phase-trajectory plane diagrams, and Poincaré diagrams of the membrane system are obtained. The results show that the anisotropic coefficient, dimensionless air drag, and dimensionless temperature significantly impact the investigated nonlinear dynamic of the anisotropic membrane, which provides a theoretical basis for production efficiency and high-quality printing equipment. [ABSTRACT FROM AUTHOR]

Currently, immunotherapy is seen to be the most effective cancer treatment. This is especially true while treating chronic lymphocytic leukemia (CLL), a slow-growing B-lymphocyte neoplasm that gradually compromises the immune system. Mathematical modeling is acknowledged as a key technique for analyzing theoretical and practical challenges in this field of cancer research and others. We were inspired to develop a mathematical model because of its dearth in investigations of chemotherapy-induced immunotherapy for CLL. This study effort formulates the dynamics of lymphocytic leukemia utilizing fractional calculus to conceptualize the complex processes of this viral illness. The basic idea of fractional calculus has been shown using the Atangana–Baleanu framework. For the suggested model's chaotic and dynamic behavior, a new numerical approach is described. We inspect the stability and convergence of the suggested numerical technique in our work. The fluctuation of various system input elements has demonstrated the oscillatory and chaotic behavior of the system. Moreover, we have demonstrated how the suggested mechanism of lymphocytic leukemia infection is affected by fractional order. Through numerical simulations, the most important input parameters are emphasized, and the policymakers are given control intervention suggestions. [ABSTRACT FROM AUTHOR]

This research presents a comprehensive investigation into the electromagnetic compatibility (EMC) analysis of rail vehicle speed sensors. It begins by establishing rigorous EMC testing standards for radio field speed sensors used in railway vehicles, encompassing parameters such as antenna orientation, interference strength, frequency range, and signal stability. Additionally, the study explores the theoretical underpinnings of radio frequency (RF) emissions, emphasizing the importance of loop size in PCBs with transmission lines and the complexities involved in estimating field strength. Notably, the research introduces the integration of quantum-based 3D reconstruction algorithms into EMC analysis, enabling a more accurate representation of the electromagnetic environment surrounding rail vehicles. Furthermore, an optimization algorithm based on chaos theory and neural networks is proposed, offering a promising approach to fine-tune sensor design for enhanced EMC compliance. Through experiments and tests, the study demonstrates the significant impact of optimization and quantum-enhanced 3D reconstruction on the EMC of rail vehicle speed sensors, resulting in reduced RF radiation and improved electromagnetic compatibility. This research contributes to the advancement of EMC analysis in the railway industry, ensuring the safety and performance of critical components. [ABSTRACT FROM AUTHOR]

In this research work, we investigate a new three-dimensional jerk system with three parameters in which one of the nonlinear terms is a sinusoidal nonlinearity. We show that the new jerk system has two unstable equilibrium points on the x-axis. Numerical integrations show the existence of periodic and chaotic states, as well as unbounded solutions. Consideration of the Poincaré sphere at infinity found no periodic states. We show that the new jerk system exhibits multistability with coexisting attractors. We also present results for the offset boosting of the proposed chaotic jerk system. Using MultiSim version 14.1, we design an electronic circuit for the new jerk system with a sinusoidal nonlinearity. As a control application, we design complete synchronization for the master-slave jerk systems using backstepping control technique. Simulations are presented to illustrate the main results of this research work. [ABSTRACT FROM AUTHOR]

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This document is a research article that discusses the synchronization of a 4D hyperchaotic system using the Active Disturbance Rejection Control (ADRC) method. The study compares ADRC with the Proportional-Integral-Derivative (PID) control method and optimizes the coefficients of both methods using the Particle Swarm Optimization (PSO) algorithm. The results show that ADRC successfully maintains synchronization even in the presence of disturbances, while PID fails to do so. The article emphasizes the importance of chaos control and synchronization in various fields and discusses the challenges of controlling 4D chaotic systems. The research was funded by Balikesir University and the data generated during the study is available. [Extracted from the article]

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This study introduces the Chaotic Particle Swarm Optimization as an innovative variant of the traditional particle swarm optimization algorithm, addressing the issue of particle swarm optimization getting trapped in local minima with a low convergence characteristic during later iterations. Chaotic particle swarm optimization incorporates principles from chaos theory to enhance the swarm's exploration and exploitation capabilities. By introducing controlled chaotic behavior, particles exhibit more diverse and unpredictable movements in the search space, leading to improved global convergence and escape from local minima. The proposed method has been implemented and evaluated on benchmark problems to assess its effectiveness. The integration of chaos theory with particle swarm optimization offers promising opportunities for developing robust and efficient optimization techniques suitable for complex and dynamic problem domains in various real-world applications. [ABSTRACT FROM AUTHOR]

ABSTRACT The autonomic nervous system is closely linked to heart rate and is characterized as a chaotic deterministic system. As the heart is therefore controlled by a non-linear system, these analyzes are being used more and more. The aim of this study was to evaluate nonlinear indices of recurrence graphs and linear indices in healthy, sick and at risk of death dogs and to demonstrate whether these indices have good diagnostic accuracy to identify dogs at risk of death. Sixty-six dogs underwent heart rate variability analysis using a frequency meter. The results showed that the SDNN, RMSSD, PNN50% and DET% indices showed a significant difference between all groups, helping to differentiate the health status in terms of autonomic homeostasis. Greater sensitivity (96.67%) was observed for linear indices (SDNN, RMSSD and PNN50%) and greater specificity (100%) for non-linear indices (DET%, REC% and LAM%) in the recognition of dogs at risk of death. Linear indices (SDNN, RMSSD and PNN50%) and non-linear indices (DET% and ShanEnt) showed greater diagnostic accuracy for identifying healthy or dying dogs. It is concluded that the studied indices of heart rate variability help to differentiate the health status in healthy dogs and are excellent predictors of prognosis.

This study draws on the parallelism between digitalization and the complexity of the Islamic banking industry (IBs) in a post-pandemic era. It examines the digital Butterfly Effect on the Islamic banking industry to promote tech-driven IBs through an empirical lens. The study constructs a Fintech adoption index (FADi). It uses a Bayesian vector Auto-Regressive model, causality tests and impulse response functions for yearly data from 2008 to 2022 to examine the possible magnified effect of adopting Fintech by the Islamic banking industry in Malaysia. Key findings suggest that embracing Fintech by the IBs enhances the profitability of the banks, which is measured by the return on asset and return on equity. In addition, the study reports a ripple effect of FADi on the broader spectrum of the Malaysian economy. This indicates that Fintech fosters economic growth, household consumption, financial and insurance services, and corporate taxes. On the other hand, Fintech adoption helps reduce the unemployment rate. The findings contribute to the literature by investigating the IB as a system within financial chaos theory and the possible Butterfly Effect triggered by Fintech adoption.

Qualitative analysis in mathematical modeling has become an important research area within the broad domain of nonlinear sciences. In the realm of qualitative analysis, the bifurcation method is one of the significant approaches for studying the structure of orbits in nonlinear dynamical systems. To apply the bifurcation method to the (2 + 1)-dimensional double-chain Deoxyribonucleic Acid system with beta derivative, the bifurcations of phase portraits and chaotic behaviors, combined with sensitivity and multi-stability analysis of this system, are examined. Initially, the bifurcations of phase portraits are visually identified at the obtained equilibrium points of a planar dynamical system via both Hamiltonian and Jacobian algorithms. The obtained results indicate Jacobian algorithm is more efficient in identifying the stability of bifurcations than the Hamiltonian algorithm for this system. Subsequently, by introducing an external perturbation term into the planar dynamical system, the chaotic behavior is effectively identified by using a variety of tools, such as two- and three-dimensional phase portraits, time series, Lyapunov exponents, and Poincaré maps. The findings suggest that the perturbed dynamical system deviates from regular patterns and exhibits behavior ranging from periodic to quasi-periodic and from quasi-periodic to chaotic. Finally, the sensitivity and multi-stability of the system are examined using the Runge-Kutta method to assess the model's response to minor variations in initial conditions through numerical solutions, revealing that the model is sensitive and multi-stable. The outcomes of this study will enhance a relationship between applied mathematicians and experimental biologists, helping to explore hidden features of Deoxyribonucleic Acid through the studied model.

The article focuses on the dramatic elements in Raymond Chandler's "The Big Sleep," particularly in chapters 14-16, highlighting their structure as a three-act farce. Topics include the use of Chekhov's gun to advance the plot, the farcical and chaotic nature of the scenes involving multiple guns, and Chandler's commentary on the impact of gun violence in 1930s Los Angeles.

Load carriage experiments are typically performed from a linear perspective that assumes that movement variability is equivalent to error or noise in the neuromuscular system. A complimentary, nonlinear perspective that treats variability as the object of study has generated important results in movement science outside load carriage settings. To date, no systematic review has yet been conducted to understand how load carriage dynamics change from a nonlinear perspective. The goal of this systematic review is to fill that need. Relevant literature was extracted and reviewed for general trends involving nonlinear perspectives on load carriage. Nonlinear analyses that were used in the reviewed studies included sample, multiscale, and approximate entropy; the Lyapunov exponent; fractal analysis; and relative phase. In general, nonlinear tools successfully distinguish between unloaded and loaded conditions in standing and walking, although not in a consistent manner. The Lyapunov exponent and entropy were the most used nonlinear methods. Two noteworthy findings are that entropy in quiet standing studies tends to decrease, whereas the Lyapunov exponent in walking studies tends to increase, both due to added load. Thus, nonlinear analyses reveal altered load carriage dynamics, demonstrating promise in applying a nonlinear perspective to load carriage while also underscoring the need for more research. [ABSTRACT FROM AUTHOR]

Complex systems consist of many components that interact with each other, and nonlinearity is fundamental in the dynamics that arise as a result of the interaction of these components and cannot be studied by observing only a small part of the system. A large number of them make fluctuations an integral part of their dynamics. Through interdisciplinary research, we integrate different disciplines and methodological approaches. We study complexity from different angles through topics that include neuroscience, artificial intelligence, and quantum physics. We have sought to explore these topics that have gained progressive interest in scientific circles as well as outside academic circles, influencing many areas outside academic research. Two goals connect our research. First, theoretical insights from neuroscience, artificial intelligence and quantum physics of the financial stock market. "Financial stock markets are sophisticated machines intertwined with scientific networks" (Ana Negovanović, 2024). They are the core of a system of different blocks that interact on the financial market in an interdisciplinary interaction of the most complex structures, neural networks with interconnected nodes. Second, new technologies- convergence of technologies, new industries, space industry through chaos theory. Investigating the attributes of complex systems is structure. Systems are structured in such a way that some parts of the system are specialized, and systems can naturally be divided into different levels of organization, which should be modeled at different levels of detail. An important component of systems understanding is the ability to break down a system model into its component parts and levels to see how the parts behave and how to connect the parts and levels to understand the overall dynamics and structure of the system. Perhaps one of the most transparent examples of the importance of structure in thinking about complex systems is the space program, where one must equally consider the behavior of individual components and the dynamics of how those components interact with each other.

In this paper, a novel image encryption scheme is presented that leverages a combination of hyperchaotic systems, Singular Value Decomposition (SVD), RC5 operations, permutation techniques, and a custom S-box generated via the XORshift algorithm. Multiple satellite images are merged into a single augmented image prior to encryption by this algorithm, effectively protecting against traffic analysis attacks that could compromise individual encrypted images. Once the augmented image is created, it is split into RGB color channels, and each channel undergoes a four-stage encryption process. The encryption process is initiated by the generation of a chaotic sequence from a six-dimensional (6D) hyperchaotic system. This initial key sequence is then manipulated and transformed into a new key using SVD. The transformed key sequence is utilized to XOR the original image, providing an initial layer of encryption. Subsequently, the image is divided into blocks, and RC5 operations are applied to each block to enhance the security of the encryption process. Following this, a permutation operation is performed on the image using the chaotic sequence generated earlier. Finally, an S-box, created from a random sequence generated by the XORshift algorithm, is applied to the image to further obscure the pixel values. The robustness of the algorithm is validated by numerical tests, demonstrating its effectiveness against both statistical, differential attacks and brute-force attacks, making it extremely difficult for third parties, such as cloud service providers, to identify any relational patterns between the encrypted satellite images. Specific numerical values that demonstrated an enhanced security level include a key space of $2^{7016}$ , entropy exceeding 7.999, and a cross-correlation of $\approx 0$ . This encryption method not only strengthens the protection of satellite imagery against unauthorized access but also ensures the integrity and confidentiality of the images, which are crucial for applications ranging from national security to environmental monitoring in an increasingly data-driven world.

In the 21st century, the digital era, chaotic systems become the backbone in designing the secure ciphers for image cryptography because of their intrinsic features like dynamical behavior and sensitivity to initial conditions. In this regard, 1-dimensional (1D) non-linear dynamical systems are one of the most studied in chaos theory. Besides the advantages of 1D chaotic systems, these systems have short periods and a short range of control parameters. A new 1D chaotic system called as Cosine Chaotic Equation (CCE) was developed to address this issue. The new and simple chaotic system has a larger range of control parameters $\alpha $ which increases the key space to make brute force attacks infeasible. The system is rigorously tested using the randomness evaluation metrics SP800-22 test suite recommended by the National Institute of Standards and Technology (NIST). It proved itself as an excellent addition in the pool of 1D chaotic systems to use safely in designing new ciphers. The new dynamical system is applied in an image encryption technique to prove its efficacy.

This article proposes a novel double data security algorithm that first encrypts sensitive data using a two-stage encryption method based on numerical solutions from a fractional-order memristive coupled neural network system. Solutions are obtained to generate encryption keys and construct S-boxes, which are then applied along with an initial key to encrypt the data bits through repeated XOR and S-box operations. The encrypted output is then hidden imperceptibly within 3D geometries by slightly modifying model points based on the encrypted data bits. This two-pronged approach provides enhanced protection for confidential information compared to single encryption or data hiding alone. Numerical experiments demonstrate the effectiveness of encryption in obscuring patterns while data extraction from modified 3D models validates recovery with negligible visual impact. Additionally, the proposed encryption scheme is shown to be superior to the standard AES-256 algorithm in terms of both computational efficiency and security against brute-force attacks. Through a synergistic blend of robust encryption and stealthy data hiding within 3D objects, the presented algorithm can reliably ensure privacy for sensitive digital data transmissions and storage applications.

In a rapidly advancing world of technology, information security studies have become the backbone of the digital age, and steps in this area are critical. In this context, cryptography, in particular, plays a key role in ensuring the confidentiality, integrity and authentication of data. s-box structures provide a certain diversity and security layer in encryption algorithms, forming one of the key elements in this area. This study focuses on the design and analysis of s-box structures, examining the potential impact of chaos theory-based structures on encryption systems. First, it provides a comprehensive classification of existing s-box design proposals in the literature, and explores the contribution of chaos theory to the security features of these structures. The original contribution of the study is the results obtained with the help of the developed analysis and design program. The program optimizes levels of complexity, randomness, and resistance, and demonstrates the resistance of these new structures to cryptanalysis attacks. The paper also draws attention to open issues in the field of chaos-based s-box design and provides a road map for future research. It is estimated that all these findings will provide a common motivation for researchers in the relevant literature and constitute the basis for many practical practices.

ABSTRACT:This Research enables the studying of scientific essence and extracting their laws to the artist for perceiving the relationships and the systems that enriching both oF Innovation and creativity to him , In goth century , It appeared many of intellectual and philosophical theories and the chaos theory is an important of them that considered as of mathe and physical recently theary that took a curriculum in thinring throughout the total cognitive integration and recomstruction of the elements and the trace structural systems associated with shape and randomness , the research problem was identified in the followting question IS it possible to reveal some athetic solutions to the systems on which the chaos theory is based to be anew entry point for updating intellectual and technical practices in the fields of drawing and painting ? and the research was aimed to enriching and developing mental imagination broadening the artistic vision and variety of the students , and the importance of the research becomes clear to comtribute to opening the field of becomes clear to comtribute to opening the field of experimentation as one of the important entrances to finding plastic solutions based om benefiting from the chaos theory as an experimental basis for con structing contem porary porary figurative paintings .The research adopts the descriptive analyticai and empirical approach one of the results of the research is that the chaos theory is replete with aesthetic solutions that enrich intellectual and technical practices . The research recommends deepening the study of scientific theories and searching for innovative performance methods in various branches of plastic art in general and in the field of drawing and painting in particular .

As a pivotal element in market mechanisms, carbon trading is increasingly recognized as crucial for achieving China's Carbon Peaking and Carbon Neutrality Goals. This study introduces a comprehensive dynamic model, integrating carbon trading, emissions, economic growth, and green technology innovation, to offer a holistic understanding of the interplay between these domains. Utilizing principles from nonlinear dynamics and chaos theory, the model is adept at simulating various scenarios and assessing the effectiveness of government policies in stabilizing these complex systems. In-depth analysis provided by this research sheds light on the nuanced impact of carbon trading policies on sustainable development. Key findings highlight (1) Carbon trading's essential role as a catalyst in propelling sustainable and high-quality growth. (2) A strong positive relationship is observed between the sophistication of the carbon trading mechanism and its effectiveness in stimulating green technology innovation and fostering high-quality green development. Notably, carbon trading's influence on green technology innovation markedly enhances the efficacy of carbon emission reduction strategies. (3) Government regulations are instrumental in augmenting carbon prices, thus incentivizing increased corporate participation in emission reduction and enhancing the overall impact of carbon emission reduction. Nevertheless, the study identifies a critical threshold in regulatory intensity, beyond which there is a risk of system destabilization ( a 3 ≥ 0.032 ). These findings underscore the imperative for developing an integrated national carbon emission trading market, prioritizing sustainable growth strategies and diligently pursuing China's environmental objectives. [ABSTRACT FROM AUTHOR]