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Double-circumferential-slot air bearing (DCSAB) systems provide multidirectional supporting forces and have high stiffness, increasing the stability of instruments at high rotational speeds. However, DCSAB systems may exhibit chaotic motion because of a nonlinear pressure distribution within the gas film, supplied gas imbalances, or an inappropriate design. This study investigated the occurrence of nonperiodic motion in a DCSAB system by analyzing the dynamic response of systems with different rotor masses and bearing numbers. The dynamic trajectory, spectral response, bifurcation, Poincaré map, and maximum Lyapunov exponent were analyzed to identify chaotic behavior. Behavior was found to be highly sensitive to rotor mass and bearing number; the system exhibits chaotic behavior when the rotor mass has values in three intervals within 0.1–6.0 kg given a fixed bearing number of Λ = 3.8. To reduce the computational cost of predicting chaotic behavior, the maximum Lyapunov exponent was predicted using various machine learning models; a voting model combining random forest with XGBoost has the highest performance. The results can be used as a guideline for designing of DCASB systems for use in industrial applications. • Effect of rotor mass and bearing number on slots air bearing system is analyzed. • Complex periodic, non-periodic and chaotic motion behavior is observed. • Chaos occurs at specific rotor mass and bearing number proven by Lyapunov exponent. • Voting model combining random forest and XGBoost obtains better prediction accuracy. [ABSTRACT FROM AUTHOR]

A new problem at the intersection of multi-agent systems, chaotic time series prediction, and flow map learning is formulated in this paper. The problem involves agents collaborating to track moving targets in chaotic dynamic systems by communicating. Inspired by the multi-scale hierarchical time-stepper (HiTS), a novel Distributed Prediction Network based on Multi-scale Attention (DPNMA) is proposed to fuse predictions from agents at different scales through an enhanced self-attention mechanism. The experimental evaluation demonstrates that DPNMA effectively mitigates cumulative errors and enhances the accuracy and robustness of the predictions, which has important implications for the scenarios where the agents have heterogeneous and constrained capabilities. [ABSTRACT FROM AUTHOR]

In this work, an autocatalytic chemical reactions model with mutation is investigated, and a nonlinear control is proposed to lead the system to a behavior that maintains the system with a desired behavior and with suppress the chaotic behavior. Numerical results considering a broad analysis of the system parameters confirmed the chaotic behavior using phase portraits, bifurcation diagrams and Lyapunov exponents. An analysis of the system behavior in fractional order considering the Atangana–Baleanu–Caputo operator was performed to include the memory effect in the system dynamics. The numerical results obtained demonstrated that the system is extremely sensitive to variations in the order of the derivative, taking the system from chaotic behavior to periodic behavior with small variations in the order of the derivative. The chaotic behavior of the system is proven in fractional order by the 0–1 test and a scale index based on the wavelets test. The proposed control demonstrated to be efficient in maintaining the main product (ethanol) output concentration at the desired level. • Observation of chaotic behavior in bioreactors • Influence of fractional order on the dynamics of nonlinear systems • Application of control in the optimization of biological processes [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order hyperchaotic system based on dual memristors is proposed by introducing flux-controlled and charge-controlled memristors into a simple RLC circuit. Dynamics of the hyperchaotic system are investigated using bifurcation diagrams, Lyapunov exponents spectrum (LEs), phase diagrams, time-domain diagrams, spectral entropy (SE) and C 0 complexity. The results show that it has a plane of equilibria and exhibits rich dynamical characteristics, including hyperchaos, homogeneous and heterogeneous extreme multistability. Meanwhile, the transient transition phenomena as well as the effect of parameters on the complexity and chaotic behavior of the system are also studied. Furthermore, the practical implementation of the system is realized through analog and digital circuit. The experimental results validate the correctness of the theoretical analysis and help to make better use of the hyperchaotic system in applications such as secure communications. • A fractional-order hyperchaotic memristive system with infinite equilibrium point is proposed • Compared with integer-order system, the fractional-order system has stronger chaotic characteristics and higher complexity • The system exhibits homogeneous and heterogeneous extreme multistability behavior • The proposed system is implemented by analog circuit and digital circuit [ABSTRACT FROM AUTHOR]

Optimization techniques are required to find the best solutions to challenging problems in many engineering disciplines. Metaheuristic algorithms that effectively increase search performance using various evolutionary strategies have become increasingly popular in recent years. The Golden Sinus Algorithm (GoldSa) is a population-based optimization algorithm that uses the sine function and the golden ratio. In this study, a chaotically enhanced opposition-based Golden Sinus Algorithm (Co-GoldSa) has been proposed to improve the efficiency of the exploitation and exploration ability of the GoldSa method. While designing this approach, it is first necessary to analyze the chaotic behavior of the GoldSa parameters. For this purpose, three chaotic GoldSa methods have been developed using eight chaotic maps to determine the effect of the chaotic maps on the parameters with different behaviors. Secondly, the opposition-based learning strategy is adjusted to the cGoldSa to enhance the searching ability. To investigate the proficiency of the proposed Co-GoldSa method, it has been examined with well-known and newly introduced metaheuristic approaches on benchmark functions and classical engineering design problems. Besides, an efficient framework of the multilevel thresholding image segmentation has been presented based on the Co-GoldSa method since the efficient processing of pathological images is quite important in medical diagnostics. The experimental outcomes reveal the superiority of the proposed method in solving global optimization problems, image segmentation, and engineering problems. Thus, the outcomes of the benchmark functions, image segmentation, and classical engineering problems support that the proposed Co-GoldSa approach can be considered a promising method for resolving challenging optimization problems. • Different ergodic chaotic systems are used to generate chaotic values on the parameters with different behaviors. • The Co-GoldSa method is proposed to enhance the searching ability and initial population. • The efficiency of the Co-GoldSa method is tested on benchmark functions, classical engineering problems and multilevel thresholding. • An efficient image segmentation framework is developed for pathological images. [ABSTRACT FROM AUTHOR]

Dynamical systems can be analysed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within them but weak correlation between the subsets. A system of non-linear oscillators weakly coupled in the phase approximation is studied. The informational distance maps show different regimes of collective behaviour, ranging from independent, local, and global, as the control parameters of the system are changed. This rich set of behaviours happens despite the simple nature of the model used. Complex hierarchies between oscillators can be identified near the edge of chaos region in the informational distance dendrograms. We identify the emergence of local collective regimes, further corroborated by the spatiotemporal maps. Correlation diagrams also exhibit non-trivial dependence for the system at the edge of chaos. • Surge in complexity measures at EOC signals enhancement of information processing. • Informational distance matrix can be used to identify complex correlations at EOC. • Dendrograms at EOC shows emergence of local collective behaviour. • Fine tuning can be avoided for sub-optimal improvement of information processing. [ABSTRACT FROM AUTHOR]

The forced van der Pol oscillator has played a fundamental role in the development of nonlinear science. It is notable that the van der Pol oscillator in the absence of an AC forcing term explains the underlying mechanism that induces limit cycles and relaxation oscillations; the forced van der Pol oscillator was the first electric oscillator that, via measurements of the emitted sound, was inferred to exhibit chaotic behavior (van der Pol and van der Mark, 1927). This oscillator thus had a significant influence on the development of chaos theory. It was subsequently demonstrated, via a nonstandard analysis undertaken in the 1980s, that a canard explosion was present in the dynamics exhibited by this oscillator. In previous works (Inaba and Kousaka, (2020); Inaba et al., (2023)), we established the existence of bifurcation structures that are referred to as nested mixed-mode oscillations (MMOs); these structures are generated by a forced Bonhoeffer–van der Pol (BVP) oscillator. Nested MMOs, despite their complexity, are robust, repeatable, and composed of higher dimensional oscillations. In this study, we show that nested MMOs can also be produced by the forced van der Pol oscillator. This paper is of extreme importance as it demonstrates that nested MMOs are not a phenomenon that can only be observed in specific BVP systems. Based on the fact that nested MMO bifurcations also occur in the forced van der Pol oscillator, this study indicates that nested MMOs could represent a phenomenon that is more widely observed than previously believed. • The van der Pol equation has played significant roles in nonlinear science. • Nested mixed-mode oscillations (MMOs) occur in the forced van der Pol equation. • Nested MMOs are a complex phenomenon that evidently has strong orders. • MMOs are at least doubly nested in the forced van der Pol oscillator. • This work indicates that nested MMOs are a widespread phenomenon. [ABSTRACT FROM AUTHOR]

The exploration of the nonlinear dynamics related to the new coupled Konno–Oono equation, which determines the propagation of magnetic fields, is the focus of this work. Through the employing of Lie group analysis, the bifurcation phase portraits, and chaos theory, the project will investigate symmetry reductions in dynamical systems and examine the dynamic behavior of perturbed dynamical systems. The 3D phase portrait, 2D phase portrait, Lyapunov exponent, time series analysis, sensitivity analysis, and an examination of the existence of multistability in the autonomous system under various initial conditions constitute a few of the methods used for recognizing chaotic behavior. Furthermore, the investigation constructs general solutions for solitary wave solutions, such as exponential and hyperbolic function, singular, dark, and bright soliton solutions, by using the new Kudryashov methodology to determine the investigated equation analytically. These solutions are shown graphically as 2D, 3D, and contour plots with specifically selected values. They include as well with the related constraint circumstances. Additionally, a discussion and a visual illustration of the considered equation's sensitivity analysis are presented. The observations demonstrate that the aforementioned approach is an effective procedure for treating a variety of nonlinear PDE systems that arise in nonlinear physics analytically. The plot of the Lyapunov exponents is employed to validate the chaotic dynamics of the studied model. Additionally, the multiplier method is employed to determine the conserved vectors for the analyzed problem. • Coupled Konno–Oono equation within the domain of magnetic fields is considered. • The Lie invariance condition is applied to identify symmetry generators. • Soliton solutions are derived and phase portrait analysis has been done. • Chaotic behaviors are examined with different characteristic settings. • Conserved vectors for the studied equation are calculated. [ABSTRACT FROM AUTHOR]

This paper is subjected to study the nonlinear integrable model which is the (3+1)-dimensional Boussinesq equation which has a lot of applications in engineering and modern sciences. To find and examine the analytical exact solitary wave solutions of (3+1)-dimensional Boussinesq equation, a modified generalized exponential rational functional method is exerted. As a result, waves, singular periodic, hyperbolic, and trigonometric type solutions are obtained. These acquired solutions are more innovative and encouraging to researchers in their endeavor to study physical marvels. To illustrate how some selected exact solutions propagate, the graphical representation in 2D, Contour, and 3D of those solutions is provided with various parametric values. The considered equation is additionally transformed into the planar dynamical structure by applying the Galilean transformation. All potential phase portraits of the dynamical system are investigated using the theory of bifurcation. The Hamiltonian function of the dynamical system of differential equations is established to see that, the system is conservative over time. The presentation of energy levels through graphics provides valuable insights, and it demonstrates that the model has solutions that can be expressed in closed form. The periodic, quasi-periodic, and chaotic behaviors of the 2D, 3D, and time series are also observable once the dynamical system is subjected to an external force. Meanwhile, the sensitivity of the derived solutions is carefully examined for a range of initial conditions. [ABSTRACT FROM AUTHOR]

Simple-form chaotic systems with complex behaviors have always attracted the attention of researchers. This article introduces a novel 4D chaotic system that has only a quadratic nonlinear term as compared with the existing no-equilibrium continuous chaotic ones with two quadratic or higher nonlinearity. Despite the simplicity of its model, this new system exhibits complicated chaotic behaviors. Many interesting phenomena including the coexistence of different hidden attractors, offset boosting and antimonotonicity have been discovered by various numerical analysis such as bifurcation diagrams, Lyapunov exponent spectra, and phase portraits. The further circuit simulation of this new system verifies its feasibility and practicality. Moreover, the new system is applied to construct Pseudo-Random Number Generators (PRNG), following a thorough assessment of its complexity and randomness by sample entropy. The generated numbers are subsequently assessed using 15 statistical tests. The results confirm that the new system can produce unpredictable numbers with high randomness, making it ideal for information encryption. [ABSTRACT FROM AUTHOR]

The driving mechanism of spatiotemporal chaos is one of the most important questions in the dynamics of predator-prey systems. In this paper, we investigate the spatiotemporal chaotic behaviors driven by refuge effect and their complexity in a Lotka-Volterra discrete predator-prey system. By choosing refuge effect as the bifurcation parameter, the existence conditions of Neimark-Sacker and flip bifurcations near the stable equilibrium point are analyzed. The bifurcation diagrams, maximum Lyapunov exponents, phase diagrams, diagrams of space-amplitude and space-time, spatial return maps and Kolmogorov-Sinai entropy are used to analyze the complex dynamical behaviors of the system. The results show that the refuge effect has a two-way effect on the stability of the system, and both Neimark-Sacker and flip bifurcations caused by it open the route to chaos. The increase in unpredictability of chaotic attractors makes the system increasingly chaotic characteristics. In addition, the characteristics of spatiotemporal dynamics on the route to chaos are captured. The chaotic behaviors of the system on the two types of bifurcations show transitions among several generic features, including frozen random pattern, defect chaotic diffusion pattern, pattern competition intermittency and fully developed turbulence. Our study promotes the understanding of the complex spatiotemporal dynamics of refuge-driven spatiotemporal chaos in predator-prey systems. • The refuge effect drives spatiotemporal chaos in the predator-prey system. • The system opens the route to chaos through two types of bifurcations. • The characteristics of chaos are captured and four chaotic patterns are found. • It provides a new perspective for future experiments on the refuge effect. [ABSTRACT FROM AUTHOR]

For finite time series, it is difficult to provide a convincing determination scheme for specifying relevant parameters of entropy. This article proposes a new entropy, σ k E n , based on the amplitude fluctuations of time series segments. It uses the optimal variance estimation under the principle of minimizing A M S E ( σ ˆ 2) to adaptively select the window width, and then realizes the no-argument calculation process of volatility entropy through kernel density estimation. By testing with artificial data and applying to real-world data, it has been verified anti-noise and stability properties of σ k E n. In a background noise environment with an intensity of 20%, σ k E n distinguish various chaotic systems and random signals efficiently. In addition, this manuscript also proposes the plane of (σ k E n , N k E n) and (σ ̄ , σ k E n) , which also successfully identifies 6 types of chaotic systems, and 3 random noise signals. Furthermore, (< σ ̄ > , < σ k E n >) curve exhibits different dynamical behavior patterns for these chaotic systems. Finally, we employ (σ ̄ , σ k E n) as a feature and take 8 usual machine learning models, such as Linear Discriminant, Gaussian Naive Bayes and Subspace Discriminant, etc, to perform anomaly detection and fault classification tests on 6 open datasets. Given the appropriate classifiers, our method can achieve a classification accuracy of 100% for four tasks, and an average accuracy of over 96% for the remaining two. This is significantly superior than the accuracy obtained by using Permutation Entropy as a feature. • Based on volatility of fragments, we introduce an parameter-free entropy, σ k E n. • Optimal estimator and KDE yield a stable, anti-noise complexity measurement. • Distinguish various deterministic and stochastic singles in noisy environment. • Test on 6 open dataset, get 100% accuracy in 4 diagnosis tasks, 96% in other 2. [ABSTRACT FROM AUTHOR]

Recently, the color image encryption algorithm based on chaos theory has become the focus of current research. When encrypting color images, the common practice is to treat color images as different gray components and process them severally, which results in more redundancy and low efficiency. The security of chaotic cryptosystems also depends on the performance of the chaotic systems adopted. The structures of many current chaotic systems are fixed, making their behaviors highly predictable. Additionally, the range of chaotic region parameters is limited and discontinuous. To solve the above-mentioned problems, a new color image encryption algorithm (CIEA) using fractal and chaos theory is presented, which fully considers the inherent connection among the RGB components of color images. First, we propose a variable-structure discrete hyperchaotic system (VSDHS) to solve the dilemma encountered by existing chaotic systems. The excellent dynamic properties of VSDHS are verified by rigorous mathematical proof and simulation performance analyses. Then, VSDHS-CIEA is designed using fractal theory and VSDHS. The algorithm makes full use of the inherent connection among the different components of color images and performs cross-plane confusion. Simulations and performance analyses prove that VSDHS-CIEA has higher security and better performance than some representative image encryption algorithms. [ABSTRACT FROM AUTHOR]

The paper introduces a novel memristive chaotic system characterized by an infinite number of index-2 saddle foci, enabling it to generate multiscroll chaos and exhibit extreme multistability. Bifurcation diagrams, phase portraits and other methods are employed to examine the stabilities of equilibria and complex dynamics. It shows that by modifying the function of memristor, the system can produce multiscroll attractors with varying scroll counts. Furthermore, it can be decomposed into coexisting chaotic attractors at different locations, and this decomposition is influenced by adjustments in parameters and initial values, illustrating the impact of initial-relied and parameter-relied offset boosting. With variations in the parameter, the coexisting chaotic attractors will undergo a bifurcation, ultimately transforming into coexisting periodic attractors. The image encryption application of the system is explored, introducing an efficient chaos-based algorithm applied to encrypt Internet of Medical Things (IoMT) images, followed by a comprehensive performance evaluation. • New memristive system with multiscroll chaos and offset boosting is presented. • Complex dynamics of the system are theoretically and numerically studied. • New chaos-based image encryption algorithm with high security is designed. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to examine the non-linear characteristics of the modified equal width-Burgers equation, known as the generalized Kadomtsive–Petviashvili equation, and its ability to generate a long-wave with dispersion and dissipation in a nonlinear medium. We employ the Lie symmetry approach to reduce the dimension of the equation, resulting in an ordinary differential equation. Utilizing the newly developed generalized logistic equation method, we are able to derive solitary wave solutions for the aforementioned ordinary differential equation. In order to gain a deeper understanding of the physical implications of these solutions, we present them using various visual representations, such as 3D, 2D, density, and polar plots. Following this, we conduct a qualitative analysis of the dynamical systems and explore their chaotic behavior using bifurcation and chaos theory. To identify chaos within the systems, we utilize various chaos detection tools available in the existing literature. The results obtained from this study are novel and valuable for further investigation of the equation, providing guidance for future researchers. • Application of the generalized logistic equation method to address the dynamics of solitary wave solutions for the generalized KP–MEW-Burgers equation. • Computation of the invariant transformations and symmetry reductions using Lie symmetry analysis. • Bifurcation and phase portraits of the unperturbed dynamical system using the idea of bifurcation theory of dynamical systems. • Chaos behavior of the perturbed dynamical system is identified through different chaos detecting tools using chaos theory of dynamical systems. [ABSTRACT FROM AUTHOR]

This paper introduces a real-time experimental set-up design to realize the robust synchronization of chaotic systems with Markov-Jump behavior, where the control law is designed based on a finite-time sliding-mode controller. First, master and slave chaotic systems are designed with the dynamics of biological Hindmarsh–Rose (HR) neurons using electronic circuit elements. In order to create the Markov-Jump behavior, the printed circuit board is adjusted to add or remove the resistors so that it is possible to obtain the time-varying dynamic of a chaotic system in the synchronization process. In the realization of chaotic neurons, Matlab and Multisim environments are used for the simulations, and Proteus software is utilized for the design of PCB layout. The Arduino microcontroller is used for signal processing and closed-loop control, where the states of chaotic neurons are recorded and control signals are produced and applied to the slave chaotic system to be synchronized. The real-time data corresponding to the behavior of the circuits was recorded, and Lyapunov exponents were calculated to check whether the neuron circuits are chaotic or not. Second, a sliding-mode controller (SMC) was designed to guarantee a finite-time convergence of synchronization error where its parameters are optimized using a recently developed efficient optimization method, namely the adolescent-identity search algorithm. Robust finite-time synchronization results with sliding-mode control were recorded in simulation and real-time experiments. Finally, the difficulties encountered in general and unachievable results related to experimental system design and finite-time synchronization are discussed for future studies. • Design of real-time HR neuron circuits with Markov jump dynamics. • Positive Lyapunov exponents of real-time HR neuron circuits. • Finite-time sliding-mode synchronization using analog circuit simulation. • Finite-time sliding-mode synchronization using the experimental set-up. [ABSTRACT FROM AUTHOR]

Most of the explored chaotic systems are either of dissipative or conservative behavior. The dissipative or conservative behavior of a chaotic system is governed by its divergence of volume. The system shows a dissipative nature for negative divergence whereas for zero divergence, a conservative nature is shown by the system. In most of the literature, these behaviors are shown in a chaotic system either with the change in system parameters or with the initial conditions. However, a chaotic system that can show both dissipative and conservative behavior based on the initial conditions and also on the system parameters is rare in the literature. Therefore, a novel chaotic system is proposed that can meet such peculiarities. In addition, the proposed system also possesses attractors of self-excited and hidden nature. The system is developed by using a Hamiltonian approach of modifying the skew-symmetric matrix and adjusting the rest of the system parameters to control the system divergence. The proposed system boasts the presence of heterogeneous multistability, extreme multistability and the coexistence of conservative flow and dissipative attractor. Many qualitative inspections are done using phase portraits, Lyapunov spectrums, bifurcation diagrams and Poincare maps to support the claims. Further, to demonstrate the controllability of the chaotic system a nonlinear active controller with single control input is designed. The real-time application of the proposed system is validated by the circuit simulation in NI Multisim and hardware implementation on a Arduino board. [ABSTRACT FROM AUTHOR]

In this paper, we establish the theory of propagation of chaos and propose an Euler–Maruyama method for McKean–Vlasov SDEs driven by fractional Brownian motion with Hurst parameter H ∈ (0 , 1 / 2) ∪ (1 / 2 , 1). Meanwhile, upper bounds for errors in the Euler–Maruyama method are obtained. Two numerical examples are demonstrated to verify the theoretical results. • The convergence rates of the numerical method for solving McKean–Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H ∈ (0 , 1 / 2) ∪ (1 / 2 , 1) are shown. • The corresponding propagation of chaos is obtained. [ABSTRACT FROM AUTHOR]

The chaotic jerk system represents a class of nonlinear systems with unique, varied, and interesting characteristics and behavior. In this study, we proposed a modified fractional-order chaotic Jerk system by the introduction of two novel nonlinear terms and two constant terms. The nonlinear terms introduced are the exponential and tangential functions while the two parameters are a and b. Stability analysis of the fractional-order Jerk system was used to establish the parameter ranges for chaotic behavior in the system. Chaos in the system was confirmed via the Lyapunov exponents. The bifurcation diagram with respect to the parameters, a and b , as well as the fractional order, α were examined. The synchronization of the system was implemented using the active control method. Finally, the studied novel circuit was realized using MultiSIM electronic software for experimental validation. • New novel Fractional order Jerk system with exponential and Tangential nonlinearity. • Active control for detecting complete synchronization and anti-synchronization. • Electronic realization of the new novel system using off-shelf component. [ABSTRACT FROM AUTHOR]

The article urges readers to embrace life's challenges, acknowledge their own humanity, and find beauty and purpose amidst the chaos, ultimately calling for a collective prayer for guidance and resilience.

The dynamical and chaotic behaviors of natural convection flow in the semi-annular and full-annular cylindrical domains are studied using the method of isolation by spectral expansion. For each of the flow cases, spectral models with different orders are obtained and dynamical characteristics of the flow are investigated using numerical simulations. For the semi-annular case of study, results reveal that in all the generated spectral models, chaotic solution appears, but the onset of chaos between each system requires different set of control parameters. Bifurcation diagrams are provided for all the systems which show the ranges of periodic and chaotic behavior of the flow. Strange attractors are captured for all the systems with different orders. For the lowest-order model, a Lorenz-like attractor is produced, which has two distinguishable scrolls similar to Lorenz's famous attractor and for the other high-order models, the shape of strange attractor gets different. For the full-annular case of study, the physical characteristics of the flow are obtained. The results show that the produced thermal plume on the top of annulus gets higher fluctuations as the flow Rayleigh number gets higher. At a specific Rayleigh number, the flow behavior gets completely unstable, which shows a transitional regime change. At this state of flow, the domain is dominated by several vortices. [Display omitted] • The dynamical behavior of natural convection in a cylindrical annulus is studied. • Spectral models with different orders are obtained for the fluid flow system. • Numerical simulations are made in order to capture the flow field of study. • Bifurcation diagrams are provided for the high-order spectral models of flow system. • The flow transition from a stable steady to an unstable point is discussed. [ABSTRACT FROM AUTHOR]