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This paper proposes a hybrid Modified Coronavirus Herd Immunity Aquila Optimization Algorithm (MCHIAO) that compiles the Enhanced Coronavirus Herd Immunity Optimizer (ECHIO) algorithm and Aquila Optimizer (AO). As one of the competitive human-based optimization algorithms, the Coronavirus Herd Immunity Optimizer (CHIO) exceeds some other biological-inspired algorithms. Compared to other optimization algorithms, CHIO showed good results. However, CHIO gets confined to local optima, and the accuracy of large-scale global optimization problems is decreased. On the other hand, although AO has significant local exploitation capabilities, its global exploration capabilities are insufficient. Subsequently, a novel metaheuristic optimizer, Modified Coronavirus Herd Immunity Aquila Optimizer (MCHIAO), is presented to overcome these restrictions and adapt it to solve feature selection challenges. In this paper, MCHIAO is proposed with three main enhancements to overcome these issues and reach higher optimal results which are cases categorizing, enhancing the new genes' value equation using the chaotic system as inspired by the chaotic behavior of the coronavirus and generating a new formula to switch between expanded and narrowed exploitation. MCHIAO demonstrates it's worth contra ten well-known state-of-the-art optimization algorithms (GOA, MFO, MPA, GWO, HHO, SSA, WOA, IAO, NOA, NGO) in addition to AO and CHIO. Friedman average rank and Wilcoxon statistical analysis (p-value) are conducted on all state-of-the-art algorithms testing 23 benchmark functions. Wilcoxon test and Friedman are conducted as well on the 29 CEC2017 functions. Moreover, some statistical tests are conducted on the 10 CEC2019 benchmark functions. Six real-world problems are used to validate the proposed MCHIAO against the same twelve state-of-the-art algorithms. On classical functions, including 24 unimodal and 44 multimodal functions, respectively, the exploitative and explorative behavior of the hybrid algorithm MCHIAO is evaluated. The statistical significance of the proposed technique for all functions is demonstrated by the p-values calculated using the Wilcoxon rank-sum test, as these p-values are found to be less than 0.05. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative properties of a physically extended six-dimensional Lorenz system, with additional physical terms describing rotation and density, which was proposed in [Moon et al., 2019] have been investigated. The dissipation, invariance, Lyapunov exponents, Kaplan–Yorke dimension, ultimate boundedness and global attractivity of this six-dimensional Lorenz system have been discussed in detail according to the chaotic systems theory. We find that this system exhibits chaos phenomena for a new set of parameters. It is well known that the general method for studying the bounds of a chaotic system is to construct a suitable Lyapunov-like function (or the generalized positive definite and radically unbounded Lyapunov function). However, the higher the dimension of a chaotic system, the more difficult it is to construct the Lyapunov-like function. The innovation of this paper is that we first construct the suitable Lyapunov-like function for this six-dimensional Lorenz system, and then we prove that this system is not only globally bounded for varying parameters, but it also gives a collection of global absorbing sets for this system with respect to all parameters of this system according to Lyapunov's direct method and the optimization method. Furthermore, we obtain the rate of the trajectories going from the exterior to the global absorbing set. Some numerical simulations are presented to validate our research results. Finally, we give a direct application of the results obtained in this paper. According to the results of this paper, we can conclude that the equilibrium point O (0 , 0 , 0 , 0 , 0 , 0) of this system is globally exponentially stable. [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]

This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey's growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter (θ) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter? [ABSTRACT FROM AUTHOR]

The focus of this paper is the design of open-loop control profiles for linear differentially flat systems whose model parameters are uncertain and are represented probabilistically. To account for the time-invariant model parameter uncertainties, polynomial chaos is used to derive a surrogate model which permits easy evaluation of the mean and variance of the uncertain states. A chance constrained optimisation problem is posed to minimise the terminal error of the stochastic states for a prescribed risk of not satisfying the terminal state bounds. To permit posing a convex optimisation problem, the cost function which is the residual energy is approximated by a hypercube circumscribing the hypersphere which bounds the terminal residual error. This relaxation permits posing a convex optimisation problem to arrive at the robust control profile. The proposed technique is illustrated on two examples including the benchmark spring-mass-dashpot system undergoing a rest-to-rest maneuver and a UAV undergoing a translation in a prescribed time. Parametric studies are conducted where the impact of varying the order of the polynomial chaos expansion and the degree of the parameterised control profiles are used to conclude that a 2–3 degree polynomial chaos expansion is sufficient to capture the time evolution of the mean and variance of the states which are required for the chance constrained optimisation problems. As expected, the design results in improved performance as the number of free variables used to parameterise the control profiles increases. [ABSTRACT FROM AUTHOR]

In this paper, we explore the rich dynamics in the Chen system using Runge–Kutta method and Deep Neural Networks (DNNs). Compared with the Lorenz system, we find that the first return map P of the Chen system exhibits a more complex structure of continuous regions in the Poincaré section. Moreover, the existence of six crossing blocks with respect to the second return map implies that there is a closed invariant set Λ in the Poincaré section such that P 2 | Λ is semi-conjugate to a 6-shift map, thus demonstrating remarkably chaos in the Chen system. [ABSTRACT FROM AUTHOR]

This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the C 0 algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map's states in commensurate and incommensurate cases. [ABSTRACT FROM AUTHOR]

This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. It is long known how to harness exponential sensitivity to changes in initial conditions for control purposes in classically chaotic systems. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Recently, this classical targeting has been generalized to quantum systems either by periodically countering the inevitable quantum state spreading or by introducing a control Hamiltonian, where both enable localized states to be guided along special chaotic trajectories toward any of a broad variety of desired target states. Only strictly unitary dynamics are involved; i.e. it gives a coherent quantum targeting. In this paper, the introduction of a control Hamiltonian is applied to Bose–Hubbard systems in chaotic dynamical regimes. Properly selected unstable mean field solutions can be followed particularly rapidly to states possessing precise phase relationships and occupancies. In essence, the method generates a quantum simulation technique that can access rather special states. The protocol reduces to a time-dependent control of the chemical potentials, opening up the possibility for application in optical lattice experiments. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices (three-dimensional applications are similarly possible). [ABSTRACT FROM AUTHOR]

In this paper, the Caputo fractional derivative is assumed to be the prey–predator model. In order to create Caputo fractional differential equations for the prey–predator model, a discretization process is first used. The fixed points of the model are categorized topologically. We identify requirements for the fixed points of the suggested prey–predator model's local asymptotic stability. We demonstrate analytically that, under specific parametric conditions, a fractional order prey–predator model supports both a Neimark–Sacker (NS) bifurcation and a Flip bifurcation. We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey–predator model. As the bifurcation parameter is increased, the system displays chaotic behavior. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. The suggested prey–predator dynamical system's chaotic behavior will be controlled by the OGY and hybrid control methodology, which will also visualize the chaotic state for various biological parameters. [ABSTRACT FROM AUTHOR]

A free-electron laser is a laser that has the same optical properties as a conventional laser, such as emitting beams of coherent electromagnetic radiation, which can reach high powers, but uses some very different principles of operation to form the beams. The chaotic motion of electrons causes a considerable decrease in the gain and efficiency of free-electron lasers. In this paper, the Hamiltonian of the dual-wiggler free-electron laser with and without axial guide magnetic field is constructed. Hamilton's equations of motion were derived exactly for both cases. The steady-state solution is also derived and investigated so that the initial conditions of the system are clear. The Poincaré surface-of-section maps were plotted after solving Hamilton's equations of motion numerically, where the chaotic behavior of the system was obvious when the axial field was included while the motion became regular and the Hamiltonian is integrable in the absence of the axial guide magnetic field. Regular orbits are observed clearly for large values of the axial field. [ABSTRACT FROM AUTHOR]

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]

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]

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 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]

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]

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]

One of the primary challenges in distributed systems, such as cloud computing, lies in ensuring that data objects are accessible within a reasonable timeframe. To address this challenge, the data objects are replicated across multiple servers. Estimating the minimum quantity of data replicas and their optimal placement is considered an NP-complete optimization problem. The primary objectives of the current research include minimizing data processing costs, reducing the quantity of replicas, and maximizing the applied algorithms’ reliability in replica placement. This paper introduces a hybrid chaos-based swarm approach using the modified shuffle-frog leaping algorithm with a new local search strategy for replicating data in distributed systems. Taking into account the algorithm’s performance in static settings, the introduced method reduces the expenses associated with replica placement. The results of the experiment conducted on a standard data set indicate that the proposed approach can decrease data access time by about 33% when using approximately seven replicas. When executed several times, the suggested method yields a standard deviation of approximately 0.012 for the results, which is lower than the result existing algorithms produce. Additionally, the new approach’s success rate is higher in comparison with existing algorithms used in addressing the problem of replica placement. [ABSTRACT FROM AUTHOR]

Many music therapists propose that chaos, such as destructiveness and disintegration, could thwart music therapy group processes and should be minimised or resolved. From a paradoxical approach, however, chaos is understood as a transformative complement to ordered, formative music therapy experiences. The research in this paper explored how music therapists and adolescents could engage with chaos as a resource in music therapy groups. From a paradoxical approach, the music therapist--researcher facilitated two short-term group music therapy processes with nine young South Africans from under-resourced and often violent communities, referred for committing offences. The researcher utilised crystallisation, including constructivist grounded theory, participatory action research, and abduction, to analyse how group members could engage with chaotic group experiences. Findings, constructed through a cyclical process of data collection, analysis, and inclusion of group feedback, are presented in a matrix. The matrix shows how groups could utilise chaos to explore multiple possibilities for responding to challenges. They expressed themselves courageously and played unconventional group roles through their musicking and participation. They juggled paradoxical tensions between observational and active, integrative and disintegrative, engagement styles. This supported their transformation in the group, and potentially within the chaotic South African context. Music therapists can use the matrix to support adolescents in music therapy groups to engage with chaos as a transformative resource. They can accompany young people through offering holding, resources and collaborative support. When it is safe, music therapists may allow or encourage chaos that empowers adolescents to cope with challenges independently. [ABSTRACT FROM AUTHOR]

Home area network (HAN) devices send the electricity consumption and other important data to the smart meter that must remain confidential from other devices. This paper proposes a novel one-dimensional hybrid chaotic map. The proposed map shows excellent chaotic properties when analyzed by bifurcation diagram, Lyapunov exponent & Shannon entropy. We further design an encryption strategy for data transfers between the smart meter and HAN devices. The proposed encryption scheme uses the existing lightweight key management in advanced metering infrastructure (LKM-AMI) architecture for data transfers, in which the encrypted data is transferred through an insecure channel and private keys are provided by trusted third party (TTP) through secure channels. The 2-way communication between HAN devices and the smart meter sends messages that are encrypted by using the proposed novel hybrid one-dimensional chaotic map. The encryption strategy mainly consists of three steps. In the first step, the seed and the control parameters are initialized. The second phase generates two intermediate keys using the proposed hybrid chaotic map. In the last phase, we encrypt the message by applying permutation followed by diffusion using intermediate keys. The proposed encryption strategy is resistant to various attacks. [ABSTRACT FROM AUTHOR]

Unpredictable strings are sequences of data with complex and erratic behavior, which makes them an object of interest in various scientific fields. Unpredictable strings related to chaos theory was investigated using a genetic algorithm. This paper presents a new genetic algorithm for converting large binary sequences into their periodic form. The MakePeriod method is also presented, which is aimed at optimizing the search for such periodic sequences, which significantly reduces the number of generations to achieve the result of the problem under consideration. The analysis of the deviation of a nonperiodic sequence from its considered periodic transformation was carried out, and methods of crossover and mutation were investigated. The proposed algorithm and its associated conclusions can be applied to processing large sequences and different values of the period, and also emphasize the importance of choosing the right methods of crossover and mutation when applying genetic algorithms to this task. [ABSTRACT FROM AUTHOR]

The rapid evolution of network technologies, where computer vision and the Internet seamlessly merge, poses significant challenges in safeguarding end-user data. To address the growing need for secure data in smart environments, lightweight and efficient security solutions are in high demand. Notably, the Trivium, a well-known encrypt stream cipher (eSTREAM) project, has been the target of several attacks. This paper proposes an innovative approach for fast and highly secured image encryption using byte scrambling and a modified version of the Trivium algorithm. The Henon map is utilized to generate random numbers for permutation, reducing time and increasing security. Performance is measured on 100 colour images with different several tests. The results present a fast and robust security system for the transmission process. It is more efficient than the traditional Trivium method. The encrypted-decryption time is reduced by 1:24 times, making it a quick security system for surgical telepresence and multimedia visuals. [ABSTRACT FROM AUTHOR]

In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc.) of the asymptotic laws and of convergence rates were studied. However, for basically all applications, e.g., for computer simulations, development of algorithms to study chaotic dynamical systems numerically, as well as for design and analysis of real (e.g., in physics) experiments, the exact values (or at least estimates) of constants (parameters) of the functions, which appear in the asymptotic laws and rates of convergence, are of primary interest. In this paper, we provide such estimates of constants (parameters) in the central limit theorem, large deviations principle, law of large numbers and the rate of correlations decay for strongly chaotic dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, an output dynamic game model of intertwined supply chains operating in two different countries is established. The Nash equilibrium point of the model and its stable region are obtained using nonlinear dynamic principles. The complex properties of the system, such as stability, period-doubling bifurcations, and chaos, are investigated using numerical simulations. Our results suggest that the level of output and the system's profits undergo bifurcation and chaos with an increase in the output adjustment speed. An interesting phenomenon occurs in that higher tariffs lead to the expansion of the stable range of the supply chain in the product-exporting country. The chaotic behavior of the system is sensitive to the value of the initial level of output. In supply chain competition, each supply chain firm should make suitable adjustments to the speed of output. To maintain the stability of domestic markets, excessive tariffs should be avoided. It is essential that each supply chain firm evaluates the potential impacts of different initial output values when making initial decisions. Using the method of delayed feedback control, the chaotic behavior of the system can effectively be controlled. These findings offer valuable and novel insight into inter-chain competition in supply chain networks. [ABSTRACT FROM AUTHOR]

In text-based authentication, the passwords along with user names are maintained in the Authentication Data Table (ADT). It is necessary to preserve the privacy of passwords in ADT to avoid offline attacks like brute force attacks, lookup table attacks, etc. In this paper, three password protection schemes, namely Encrypted Image Password (EIP), Dynamic Authentication Data Table (D-ADT), and Extended Encrypted Image Password (EEIP) are proposed for secure authentication. In EIP, the input passwords are first converted to hashed passwords and then transformed into images. Next, these image passwords are encrypted using a novel image password encryption system using chaos functions and confusion-diffusion mechanisms. In D-ADT, the hashed passwords are encrypted using a random key. The major highlight of this scheme is that during every log, the hashed password is encrypted with a new random key while keeping the plain password same as it is. So, during each login of the user, the old encrypted password is replaced with a new encrypted password in the authentication data table. The EEIP scheme combines both approaches. Passwords are converted to images and image passwords are encrypted with the new random key at every login. Performance and security analysis are carried out for the proposed algorithm concerning correlation analysis, differential analysis, entropy analysis, computation time, keyspace, and offline attack analysis. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive predictive control for controlling and stabilizing fractional order chaotic systems around the equilibrium point is provided. The stability of fractional order chaotic systems around equilibrium points in the presence of parameter uncertainty has been demonstrated using Lyapunov's stability theorem. In addition, the uncertain parameters of fractional order chaotic systems are calculated using appropriate adaptive methods based on the proposed predictive controller structure. Rossler and Chen systems were considered to numerical simulations. The results demonstrated the adaptive predictive control method's usefulness and performance. [ABSTRACT FROM AUTHOR]

This paper introduces a new 3D chaotic attractor in a gene regulatory network. The proposed model has eighteen parameters. Formulas for characteristic numbers of critical points for three-dimensional systems were considered. We show that the three equilibrium points of the new chaotic 3D system are unstable and deduce that the three-dimensional system exhibits chaotic behavior. The possible outcomes of this 3D model were compared with the results of the Chua circuit. The bifurcation structures of the proposed 3D system are investigated numerically, showing periodic solutions and chaotic solutions. Lyapunov exponents and Kaplan-Yorke dimension are calculated. For calculations, the Wolfram Mathematica is used. [ABSTRACT FROM AUTHOR]

The Ukrainian Mathematical Journal has published a special issue dedicated to the memory of Oleksandr Mykolayovych Sharkovsky, a renowned mathematician and scholar. Sharkovsky's contributions to dynamical systems and chaos theory have had a lasting impact on mathematics and its applications in physics and other natural sciences. His most famous result, known as Sharkovsky's theorem, combines the simplicity of studying cycles of a continuous interval map with an ordering of natural numbers, known as Sharkovsky's ordering. This theorem has become a fundamental concept in the field of dynamical systems theory and is widely cited in scientific literature. The journal also includes a translation of Sharkovsky's original paper and another paper by Sharkovsky and his coauthors, making his early results more accessible to the international mathematical community. [Extracted from the article]

• 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]

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]

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]

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]

• 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]

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]

In this paper, a three-dimensional conservative system is proposed. By analyzing the Hamiltonian energy, it is concluded that it is a non-Hamiltonian conservative system. By changing the values of the parameters b, c, the system presents different attractors. Then, by studying the multiple attractors coexisting of the system under different initial values, it can be found that the system has rich coexistence phenomena by changing the parameters. There are various types of coexistence of systems with chaos and chaos coexistence, periods and periods coexistence and chaos and periods coexistence. In addition, the offset-boosting under parameter control is studied by phase diagram. By studying the complexity of the system at two different initial values, the more complex initial value is chosen as the initial state when the system is synchronized. The analog simulation circuit is implemented using Multisim, the actual digital circuit is implemented with field programmable gate array (FPGA). The Matlab phase diagram, the numerical simulation results and the simulated circuit all agree well, proving the feasibility of the new system. Finally, the system is applied to backstepping synchronization, which lays a foundation for the realization of engineering application. • In this paper, a three-dimensional conservative system is proposed. It is proved to be a non-Hamiltonian three-dimensional conservative system by Hamiltonian energy analysis. • Successful implementation of Multisim simulation and FPGA hardware proved the feasibility of the system. • Through a series of studies, it has been found that conservative systems are more conducive to confidential communication. Therefore, based on this 3D conservative system, the system is applied to backstepping synchronization. [ABSTRACT FROM AUTHOR]

Fog computing utilizes user premises resources to provide better services than traditional cloud computing. Due to the heterogeneity of fog devices, scheduling poses a challenge. This paper proposes a novel version of artificial rabbits optimization (ARO) called the Nonlinear based chaotic artificial rabbits optimization (NCARO) and utilizes NCARO for task scheduling in the fog computing environment (TSNCARO). The NCARO optimizes ARO by using chaotic and nonlinear control parameters. In the proposed method, chaotic maps are used to improve the exploratory behavior of ARO. ARO’s exploratory and exploitative behaviors are also adjusted by means of a nonlinear control parameter. Three objectives are considered: service time, cost, and energy consumption. It improves performance by prioritizing tasks according to deadlines. An extensive scenario compares NCARO and TSNCARO algorithms with other algorithms. On the basis of the comparison results, the proposed algorithms achieved the best results in terms of makespan, service time, total cost, energy consumption, carbon dioxide emission rate, and percentage of deadline satisfaction. [ABSTRACT FROM AUTHOR]

This paper investigates n -scrambled sets in the sense of distribution and Li-Yorke, focusing on the equivalence of n -scrambled sets and the existence of uncountable n -scrambled sets. For the equivalence, n -scrambled sets can imply m -scrambled sets in both senses for any 2 ≤ m < n , but their inverses require certain conditions to hold. A method is provided for constructing an uncountable n -scrambled set in the distribution and Li-Yorke senses, which also verifies the equivalence between n -scrambled sets. For the existence, it is shown that distributionally n -scrambled tuples can be derived from the weak specification property (WSP), a 1-periodic and a non-1-periodic point. And the Li-Yorke (n + 1)-scrambled tuple can be characterized by an n -scrambled tuple utilizing the SP. Finally, the uncountable Li-Yorke n -scrambled set is established based on the weak mixing, and the uncountable mean Li-Yorke n -scrambled set is induced by the shadowing and Devaney chaos. • Obtain the equivalence between n -scrambled sets in the distribution and Li-York sense. • Provide a method for constructing an uncountable n -scrambled set in two chaotic senses. • Establish criteria for the existence of n -scrambled set and n -scrambled tuple. • Present a method to induce an n -scrambled tuple by weak specification property. • Build a connection between global and local chaotic behaviors of a dynamical system. [ABSTRACT FROM AUTHOR]