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The objective of this study was to determine whether multi-microRNA analysis using a combination of four microRNA biomarkers (miR-1246, 202, 21, and 219B) could improve the diagnostic performance of mammography in determining breast cancer risk by age group (under 50 vs. over 50) and distinguish breast cancer from benign breast diseases and other cancers (thyroid, colon, stomach, lung, liver, and cervix cancers). To verify breast cancer classification performance of the four miRNA biomarkers and whether the model providing breast cancer risk score could distinguish between benign breast disease and other cancers, the model was verified using nonlinear support vector machine (SVM) and generalized linear model (GLM) and age and four miRNA qRT-PCR analysis values (dCt) were input to these models. Breast cancer risk scores for each Breast Imaging-Reporting and Data System (BI-RADS) category in multi-microRNA analysis were analyzed to examine the correlation between breast cancer risk scores and mammography categories. We generated two models using two classification algorithms, SVM and GLM, with a combination of four miRNA biomarkers showing high performance and sensitivities of 84.5% and 82.1%, a specificity of 85%, and areas under the curve (AUCs) of 0.967 and 0.965, respectively, which showed consistent performance across all stages of breast cancer and patient ages. The results of this study showed that this multi-microRNA analysis using the four miRNA biomarkers was effective in classifying breast cancer in patients under the age of 50, which is challenging to accurately diagnose. In addition, breast cancer and benign breast diseases can be classified, showing the possibility of helping with diagnosis by mammography. Verification of the performance of the four miRNA biomarkers confirmed that multi-microRNA analysis could be used as a new breast cancer screening aid to improve the accuracy of mammography. However, many factors must be considered for clinical use. Further validation with an appropriate screening population in large clinical trials is required. This trial is registered with (KNUCH 2022-04-036). [ABSTRACT FROM AUTHOR]

We investigate a discrete-time Chen system. First, we give the topological classifications of the fixed points of this system. Then, we analytically show that the discrete Chen system underlies a Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. We confirm the existence of a PD and NS bifurcation via the explicit PD-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory. We performed numerical simulations to confirm our analytical results. Furthermore, we use the 0-1 chaos test to quantify whether there is chaos in the system or not. At the end, the hybrid control strategy and the OGY (Ott, Grebogi, and Yorke) method are applied to eliminate chaotic trajectories of the system. [ABSTRACT FROM AUTHOR]

This paper proposes a prediction method based on chaos theory and an improved empirical-modal-decomposition particle-swarm-optimization long short-term-memory (EMD-PSO-LSTM)-combined optimization process for passenger flow data with high nonlinearity and dynamic space-time dependence, using EMD to process the original passenger flow data and generate several eigenmodal functions (IMFs) and residuals with different characteristic scales. Based on the chaos theory, each component of the PSO algorithm was improved by introducing an inertia factor to facilitate the adjustment of its search capability to improve optimization. Each subsequence of the phase-space reconstruction was built into an improved PSO-LSTM prediction model, and the output of each prediction model was summed to determine the final output. Experimental studies were performed using data from the North Railway Station of Chengdu Rail Transit, and the results showed that the proposed model can generate better prediction results. The proposed model obtained root mean square error (RMSE) and mean absolute error (MAE) of 16.0908 and 11.3704, respectively. Compared with the LSTM, the improved PSO-LSTM, the improved EMD-PSO-LSTM, and the model proposed in this paper improved the RMSE values by 25.53%, 29.97%, and 58.76%, respectively, and the MAE values by 30.41%, 40.13%, and 63.08%, respectively, of the prediction results. [ABSTRACT FROM AUTHOR]

The microcontroller implementation, controls, and synchronization of a three-dimensional (3D) autonomous system with a parabolic equilibrium point are investigated in this paper. The system in question displays a reverse period doubling route hidden chaotic attractors with two different shapes. Then, the partial and total amplitude controls of the system are achieved by inserting two parameters. A microcontroller implementation is performed in order to confirm the results obtained from the numerical simulations. It is found that the results from the numerical simulations and microcontroller implementation qualitatively agree with each other. The sliding mode controllers are designed to control chaos in the system under study. With the sliding mode control method, the numerical simulations confirm that chaos can be controlled in the 3D autonomous system with a parabolic equilibrium point. In addition, two chaotic 3D autonomous systems with a parabolic equilibrium point and the same parameters are synchronized by the use of a unidirectional linear error feedback coupling scheme. Finally, an active control technique is applied to bring about chaos synchronization between two chaotic 3D autonomous systems with a parabolic equilibrium and different parameters. [ABSTRACT FROM AUTHOR]

This paper proposes a new image encryption algorithm based on chaos map systems, hash algorithm, and Josephus permutation. The algorithm consists of chaos initialization, pixel position permutation, and pixel information diffusion. The algorithm's initialization is generated by the original image, which has a high sensitivity to the initial value. The permutation step length is composed of Josephus permutation and gray curve permutation, which completely disturbs the pixel distribution. The diffusion process is composed of cross operation and ciphertext feedback, which breaks the strong correlation between pixels. The simulation results of the encryption algorithm are used to analyze its information entropy, the correlation between elements, and other indicators. The ciphertext image is attacked in several ways, and we analyzed its defense ability. Simulation results show that the algorithm can effectively encrypt image information and has a good defense against various attacks. [ABSTRACT FROM AUTHOR]

With the swift advancement of chaos theory, the modeling, chaotic oscillations, and engineering applications of chaotic and hyperchaotic systems are important topics in research. In this research paper, we elucidate our findings of a new four-dimensional two-scroll hyperchaotic system having only two quadratic nonlinearities and carry out a detailed bifurcation study of the proposed dynamical model. Also, an electronic circuit has been constructed for the new system using MultiSim (Version 14). The implementation of the new 4-D hyperchaotic system in a field-programmable gate array (FPGA) is performed herein by applying two numerical methods, viz. Forward Euler Method and Trapezoidal Method. The experimental results show a good match with the simulated hyperchaotic attractors. We also provide details of the hardware resources used for an FPGA Basys 3 Xilinx Artix-7 XC7A35T-ICPG236C. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study and analysis of the intelligent grouping of papers in adult higher education using a random matrix approach. Using the results of random matrix theory on the eigenvalues of the sample covariance matrix, the energy of each subspace is estimated, and the estimated energy is then used to construct a subspace weighting matrix. The statistical properties of the sample covariance matrix eigenvectors are analyzed using the first-order perturbation approximation, and then, asymptotic results from random matrix theory on the projection of the sample covariance matrix signal subspace to the real signal parametrization are used to obtain the weighting matrix based on the random matrix eigenvectors. Dynamic adjustment according to the fitness of individuals in the population is performed to ensure population diversity, while the combination of the small habitat technique can avoid the algorithm from falling into early convergence. The algorithm introduces chaos theory to optimize the population initialization process and uses the dynamic traversal randomness of chaos to select individuals in the population so that the initial population is close to the desired target solution. The design of the fitness function in the genetic algorithm generally maps the objective function of the problem to the fitness function. A good fitness function can directly reflect the quality of the individuals in the group. Based on the in-depth study of the basic attributes of the test questions and the principles of test paper evaluation, the mathematical model and objective function of intelligent paper grouping are determined by the difficulty, knowledge points, and cognitive level of the test questions as the main constraints, and NCAGA is applied to the intelligent paper grouping method, which better completes the intelligent paper grouping session for the computer system architecture course. In the process of designing the intelligent grouping algorithm, for the situations of premature convergence and convergence to locally optimal solutions that easily occur in the traditional genetic algorithm, this paper adopts the approach of adaptive adjustment of crossover probability and variation probability to improve the algorithm and achieves satisfactory results. Based on extensive business research, this paper completes the requirement analysis of the online practice system based on the intelligent grouping of papers and presents the functional design and database design of the key functional modules in the system in detail. Finally, this paper conducts functional tests on the system and analyses the test results. [ABSTRACT FROM AUTHOR]

In order to further discover the hidden chaotic attractor and its generating mechanism in the Vijayakumar system, we give a generalized system showing hidden chaotic attractors which are not from homoclinic orbit or heteroclinic orbit and consider Hopf bifurcations (codimension one and two) by first Lyapunov coefficient and second Lyapunov coefficient. The existence of periodic orbits is strictly proved theoretically. We have considered the problem of Hopf bifurcation in the chaotic system with hidden attractors, which will be helpful to reveal the intrinsic relationship between the local stability of equilibria and global complex dynamical behaviors of the chaotic system. Finally, numerical simulations are obtained for showing the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

With the macroeconomy entering a new normal, many new problems are exposed in all walks of life, and the risk of default in the financial sector is also being exposed at an accelerated pace. In the context of big data, internet finance, as an important part of the financial market, also faces many risks in the process of its rapid development. Reasonable, scientific, and effective prediction and prevention of financial default risk have become a key link in the process of risk management practice in the financial industry. Based on the powerful prediction function of the neural network, this paper combined neural network and chaos theory to construct a chaotic RBF neural network. It was applied to financial default risk prediction, which made the prediction accuracy and efficiency higher. The chaotic neural network solves the shortcomings of unstable prediction in the basic neural network and can comprehensively and accurately predict the financial default risk, so as to take measures to prevent risks. The experimental results of this paper show that the accuracy rate of the chaotic RBF neural network reaches 95%, while the accuracy rates of the BP neural network and the RBF neural network are 67% and 78%, respectively. Although the prediction accuracy of these two methods is also high, it is still not as high as the chaotic RBF neural network. Therefore, it is very meaningful to choose the chaotic RBF neural network to predict financial default risk in this paper. [ABSTRACT FROM AUTHOR]

Skipping training belongs to a competitive event, which can not only lose weight but also improve the physical quality of trainers. At present, there are some problems in skipping training, such as unreasonable plan and unsatisfactory actual training effect. The original rough set method cannot solve the analysis of multivariate data in skipping training, and the ability to evaluate the training effect of skipping is poor. Aiming at the problems existing in the training of skipping rope, this paper puts forward a skipping rope training method based on a chaotic logistics algorithm, aiming at improving the training effect of skipping rope. First, the chaos theory is used to classify the training data. Different data classifications correspond to different training results, which eliminates irrelevant information in the training scheme and reduces the amount of single data analysis. Finally, the data after classification are optimized in a single stage, and the optimal results of different training items are obtained and summarized. After the MATLAB test, the chaotic logistics algorithm is superior to the rough set method in accuracy and convergence speed and meets the actual training needs. Therefore, the chaotic logic analysis method proposed in this paper is suitable for the evaluation of skipping training. [ABSTRACT FROM AUTHOR]

Sports equipment is the key to the smooth development of ice and snow sports. With the rapid development of social economy and the improvement of people's living standards, the demand for ice and snow sports equipment is increasing day by day. This article presents an improved method based on the chaos theory and the bee colony algorithm to quantify the application experience design of ice and snow sports equipment and reduce the influence of uncertain factors on the design results. First, the chaos theory can establish the dataset of application experience design and analyze the discreteness of the set. According to the bee colony algorithm, the dataset is divided into several groups, and each group obtains the best application experience design by using the design optimization strategy. Finally, the results are mixed to obtain the final experience design results. Through MATLAB simulation analysis and verification, the improved bee colony model can improve the accuracy of application experience design of ice and snow sports equipment in an uncertain environment, shorten the overall design time, and meet the requirements of application experience design of different ice and snow sports equipment. Therefore, the model proposed in this paper is suitable for the application experience design of ice and snow sports equipment. [ABSTRACT FROM AUTHOR]

This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self-exciting attractors and a separatrix in a global domain. [ABSTRACT FROM AUTHOR]

To improve the contradiction between the surge of business demand and the limited resources of MEC, firstly, the "cloud, fog, edge, and end" collaborative architecture is constructed with the scenario of smart campus, and the optimization model of joint computation offloading and resource allocation is proposed with the objective of minimizing the weighted sum of delay and energy consumption. Second, to improve the convergence of the algorithm and the ability to jump out of the bureau of excellence, chaos theory and adaptive mechanism are introduced, and the update method of teaching and learning optimization (TLBO) algorithm is integrated, and the chaos teaching particle swarm optimization (CTLPSO) algorithm is proposed, and its advantages are verified by comparing with existing improved algorithms. Finally, the offloading success rate advantage is significant when the number of tasks in the model exceeds 50, the system optimization effect is significant when the number of tasks exceeds 60, the model iterates about 100 times to converge to the optimal solution, the proposed architecture can effectively alleviate the problem of limited MEC resources, the proposed algorithm has obvious advantages in convergence, stability, and complexity, and the optimization strategy can improve the offloading success rate and reduce the total system overhead. [ABSTRACT FROM AUTHOR]

In order to combine chaos theory and machine learning technology to predict sports performance, a research on sports performance prediction based on chaos theory and machine learning is proposed. This paper takes the sports performance as the goal to predict the data; introduce the chaos theory algorithm, and combine the neural network system and particle swarm optimization algorithm to actively train sports results and ensure the quality of performance prediction. The comparison between shot put data prediction and real data shows that the prediction results given by the model have little deviation and can provide technical services for performance prediction for special sports training. When predicting the sports performance of college students, the prediction accuracy of sports performance of each subject is no less than 90%, which proves that this system can be used in college sports management. The delay time of the model data is short, which is mainly related to the correlation coefficient. When the coefficient is determined to be 0.02, the prediction delay time is 5 s, which can effectively complete the prediction and analysis of sports performance. The combined model has various technical advantages such as chaos theory, neural system, and particle optimization. It has strong sports performance prediction ability and can provide technical support for performance prediction for athletes' training, college sports management, and other related sports industries. [ABSTRACT FROM AUTHOR]

The sports industry is an emerging industry with broad development prospects, and it is also full of competition. The sports industry has the characteristics of fluctuation, intermittence, and randomness, which are suitable for the analysis of chaos theory in order to find out the internal development law of the sports industry. In order to solve the above problems, an improved chaos theory method is proposed in this paper and the K-cluster analysis method is integrated into chaos calculation, in order to reduce the occurrence rate of the "local extreme value" and improve the accuracy of calculation results. The model uses nonlinear and irregular chaos theory to analyze the aggregation degree of sports industry, industrial spatial distribution, and the spatial governance effect and find out the best optimization decision. When selecting the optimization indicators, not only the European distance of each indicator cluster but also the spatial correlation of the indicators are considered to realize the comprehensive analysis of the sports industry and improve the accuracy of optimization. In the simulation analysis of optimization decision-making, the decision-making model based on chaos theory is compared with the previous first-order decision-making model. The results show that the improved chaos theory can control the data aggregation range of sports industry between (0∼3), the data fusion degree of industrial space between 95 and 99%, and the variation range between 0 and 0.2%, which is significantly better than (0∼9), 90∼95%, and 0∼0.4% of the genetic algorithm. Therefore, the aggregation degree, spatial governance, and decision optimization of the optimization decision-making model proposed in this paper are better than those of the previous genetic algorithm. [ABSTRACT FROM AUTHOR]

An enterprise's development and growth are inextricably linked to rational and efficient resource integration and optimization. This study focuses on the reorganization and integration of industrial elements inside the firm from the standpoint of resource integration. The ideal resource integration strategy is investigated by integrating the industrial parts of a certain enterprise in order to increase the efficiency of project completion and lower enterprise expenses. The enterprise's internal material and human resources are limited, but it is frequently necessary to execute numerous activities at the same time, and each activity must meet multiple goals. This research investigates how to properly integrate and schedule resources while attaining different goals. This research proposes using an enhanced particle swarm optimization technique (IPSO) to combine firms' internal resources. In order to address the issue of uneven particle dispersion caused by random population initialization, IPSO incorporates chaos theory into particle population initialization. The logistic mapping sequence generates a huge number of particles, and the particles with the highest quality are chosen for initialization. This can increase particle quality, allowing particles to be spread equally during setup. In the late stage, the classic particle swarm optimization algorithm (PSO) has a slow convergence rate, causing the algorithm to readily slip into a local optimal solution. This research proposes a dynamic inertia weight update approach based on fitness value. In the later stages of the algorithm, this strategy can improve the convergence speed and quality of the global optimal solution, allowing the particles to do a global search and eventually identify the population's ideal solution. Furthermore, IPSO creates a fitness function depending on task completion time. IPSO is used to test the performance of an enterprise's resource integration case. Experiments show that the method utilized can swiftly locate the ideal solution, complete the integration, and optimization of enterprise resources in the shortest job completion time, and for the least amount of money. [ABSTRACT FROM AUTHOR]

To address the shortcomings of the whale optimization algorithm (WOA) in terms of insufficient global search ability and slow convergence speed, a differential evolution chaotic whale optimization algorithm (DECWOA) is proposed in this paper. Firstly, the initial population is generated by introducing the Sine chaos theory at the beginning of the algorithm to increase the population diversity. Secondly, new adaptive inertia weights are introduced into the individual whale position update formula to lay the foundation for the global search and improve the optimization performance of the algorithm. Finally, the differential variance algorithm is fused to improve the global search speed and accuracy of the whale optimization algorithm. The impact of various improvement strategies on the performance of the algorithm is analyzed using different kinds of test functions that are randomly selected. The particle swarm optimization algorithm (PSO), butterfly optimization algorithm (BOA), WOA, chaotic feedback adaptive whale optimization algorithm (CFAWOA), and DECWOA algorithm are compared for the optimal search performance. Experimental simulations are performed using MATLAB software, and the results show that the improved whale optimization algorithm has a better global optimization-seeking capability. The improved whale optimization algorithm is applied to the distribution network fault location of IEEE-33 nodes, and the effectiveness and accuracy of the distribution network fault zone location based on the multistrategy improved whale optimization algorithm is verified. [ABSTRACT FROM AUTHOR]

Regarding a nonlinear Zener model with a viscoelastic Maxwell element as the research object, the complicated dynamic behaviors such as homoclinic bifurcation and chaos under harmonic excitation are investigated. At first, the analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on the Melnikov method. Then, the system parameters that meet the analytical condition and the main resonance condition are selected for the numerical simulation. From the bifurcation diagrams and the largest Lyapunov exponents, it is found that the homoclinic orbit breaks, and the system goes to chaos in a crisis way when the excitation amplitude passes the first threshold. The system enters another new chaotic state in the form of period-doubling bifurcation with the increase of the excitation amplitude. At last, the effects of nonlinear term, stiffness coefficient and damping coefficient of Maxwell element on the analytically necessary condition for chaos are analyzed, respectively, and the correctness of the analytical result is proved by numerical simulation. The research result shows that the critical excitation amplitude decreases with the increase of nonlinear term. In addition, the chaotic threshold increases first and then tends to remain unchanged with the raise of stiffness coefficient. The chaotic threshold increases first and then decreases with the enhancement of damping. These results provide a theoretical basis for the research of nonlinear viscoelastic system in the future. [ABSTRACT FROM AUTHOR]

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator's population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold curve is obtained by calculation and numerical simulation. The accuracy of the analytical result is proved by some typical numerical simulation results, including the local bifurcation diagrams, phase portraits, Poincaré maps, and the largest Lyapunov exponents. The effects of excitation frequency and time delay of the displacement feedback are analytically discussed. It could be found that the critical excitation amplitude will increase obviously with the increase of the excitation frequency, and under the selection of certain parameters, the critical excitation amplitude takes the time delay of 0.58 as the inflection point, which decreases at first and then increases. [ABSTRACT FROM AUTHOR]

In this study, complex dynamics of Briggs–Rauscher reaction system is investigated analytically and numerically. First, the Briggs–Rauscher reaction system is reduced into a new nonlinear parametric oscillator. The Melnikov method is used to derive the condition of the appearance of horseshoe chaos in the cases ω = Ω and ω ≠ Ω. The performed numerical simulations confirm the obtained analytical predictions. Second, the prediction of coexisting attractors is investigated by solving numerically the new nonlinear parametric ordinary differential equation via the fourth-order Runge–Kutta algorithm. As results, it is found that the new nonlinear chemical system displays various coexisting behaviors of symmetric and asymmetric attractors. In addition, the system presents a rich variety of bifurcations phenomena such as symmetry breaking, symmetry restoring, period doubling, reverse period doubling, period-m bubbles, reverse period-m bubbles, intermittency, and antimonotonicity. On the contrary, emerging chaotic band attractors and period-1, period-3, period-9, and period-m bubbles routes to chaos occur in this system. [ABSTRACT FROM AUTHOR]

We propose in this paper an investigation of the dynamical behaviors of a duopoly model with two Internet services providers (ISPs). The competition between them is assumed to take place in terms of their pricing decisions and their number of cached items. According to the ISPs' rationality level, we consider a scenario where both ISPs are bounded rational. Each ISP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamic system induced by bounded rationality and establish a necessary and sufficient condition for the stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control. [ABSTRACT FROM AUTHOR]

A mathematical model to describe the dynamic of a multiserotype infectious disease at the population level is studied. Applied to dengue fever epidemiology, we analyse a mathematical model with time delay to describe the cross-immunity protection period, including a key parameter for the antibody-dependent enhancement (ADE) effect, the well-known features of dengue fever infection. Numerical experiments are performed to show the stability of the coexistence equilibrium, which is completely determined by the basic reproduction number and by the invasion reproduction number, as well as the bifurcation structures for different scenarios of dengue fever transmission in a population. The model shows a rich dynamical behavior, from fixed points and periodic oscillations up to chaotic behaviour with complex attractors. [ABSTRACT FROM AUTHOR]

The chaotification method can be used to weaken the line spectra component of the ship's radiated noise. The main obstacle that plagues the engineering realization of this innovative concept is how to realize the small-amplitude chaotic motion of the nonlinear vibration isolation system (NVIS) in a large parameter range and how to maintain the chaotic state under variable operating conditions. In this paper, the dimensionless dynamic equation of the NVIS with a flexible base is derived. A control method similar to generalized synchronization is used to realize the continuous chaos of the system. The maximum Lyapunov exponent, the conditional Lyapunov exponent, and disturbances are introduced to verify the effectiveness of the control method and its stability and robustness in a large range of parameters. Aiming at the coexistence of multiple attractors, a new global analysis method is proposed, which is used to study the distribution of basin of attraction (BA). According to the changes of BA before and after the system is controlled, the BA is partitioned. Initial conditions from different partitions are selected to study the attenuation effect of line spectra and vibration, and the favorable initial conditions for realizing the small-amplitude chaotic motion of the system are given. The method may be extended to the global analysis of other controlled systems. [ABSTRACT FROM AUTHOR]

Conventional statistical models provide inaccurate predictions of concrete crack openings because they do not consider the nonlinear temperature response and the residual characteristics of concrete. To address this problem, this study introduces a nonlinear temperature factor and develops an improved statistical model of crack openings. The chaotic characteristics of residual time series of the improved statistical model are analyzed based on chaos theory and phase-space reconstruction theory. These theories are integrated with back-propagation (BP) artificial neural networks and genetic algorithms (GAs) to establish a GA-BP neural network model for predicting residuals. Finally, a hybrid model is developed for predicting the concrete crack opening behavior. The predictions of the conventional statistical model, the statistical model considering nonlinear temperature component, and the hybrid model are compared using the case study on the crack openings of a regulating sluice. The results show that the proposed hybrid model in this study for predicting concrete crack openings is significantly more accurate than the conventional statistical model and the statistical model considering nonlinear temperature component. [ABSTRACT FROM AUTHOR]

In this paper, the hinge in the articulated structure is studied, the gap hinge is described as a nonlinear bilateral constraint, and the equivalent modeling and analysis of the hinge connection collision vibration are carried out based on the Lankarani–Nikravesh nonlinear contact force model. With the help of the method of nonlinear system dynamics analysis research, the Poincaré mapping of hinge joint collision vibration is constructed, the bifurcation diagram of the system with different parameters is solved, and the variation law of the system motion and the influence of parameters are analyzed by combining the time response diagram, phase diagram, Poincaré cross section diagram, and spectrum diagram of the typical motion of the system. The simulation results show that the system moves in a single degree of freedom and varies with parameters with multiplicative period bifurcation and rubbing edge bifurcation leading to chaos; the system's periodic motion has shock state mutation and mirror jump transformation. [ABSTRACT FROM AUTHOR]

Supported by a third-party capacity sharing platform, manufacturers can share capacities with others to match the rapidly changing demand. Both the capacity requestor and the capacity provider can choose to seek or wait for matches, forming different trading strategies (capacity- and demand-driven strategies). Based on the game and chaos theories, this paper analyzes the preference of the capacity provider, the capacity requestor, and the capacity platform operator on different trading strategies from the aspects of profitability and stability. It finds that the platform operator values stability much more than profitability, although the latter may reach higher optimal expected profits. The preference of each supply chain member is influenced by the production cost, potential market size, and the limited capacity of the capacity requestor. A stable system can result in higher long-run profits than a profitable system. We further propose the all-win situation for the capacity provider, capacity requestor, and platform operator. [ABSTRACT FROM AUTHOR]

Direct power control (DPC) of pulse width modulation (PWM) is often used to control the instantaneous power of rectifiers. The instantaneous power contains both grid voltage and current information, and its value is not affected by coordinate transformation. It is constant in steady state and reflects the DC control characteristics. However, the switching frequency of traditional DPC is not fixed, the DC voltage has static error, and the system fluctuates greatly. In this work, we introduce the concept of stator flux of the AC motor into the PWM rectifier. Combined with the space vector PWM (SVPWM) technology, we use the virtual flux estimation method to obtain the instantaneous power value, which saves the grid voltage sensor, eliminates the static difference of DC voltage. Furthermore, considering that the neural proportion integral differential (PID) control depends heavily on the initial weight coefficient of the network, we use chaos particle swarm optimization (CPSO) algorithm, which combines the basic PSO algorithm and chaos theory to optimize the initial weight coefficient of neural PID control. In the experiment, the results prove that the performance of the controller can be effectively improved. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.13 for the incommensurate order case. Also, period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.57 for the incommensurate order case. Also, the period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results. [ABSTRACT FROM AUTHOR]

Limited by traditional construction project management ideas and systems, the implementation of the PMC model in China still has serious problems such as opposition and frequent conflicts. How to reveal the causes of organizational conflicts and explore the key mechanism of the implementation of the PMC model from the system perspective are urgent problems to be solved. Based on the idea of engineering system view, this paper abstracts the PMC project participants with self-organizing characteristics of the organizational management system, in which the internal structure is closely related, and defines the connotation of synergy and synergistic evolution of the PMC project organizational management system. Using the Cucker–Smale model to describe the group movement, the hierarchical system and the acceleration efficiency function of the project legal person's free will are constructed, and the structure, movement, and development law of the system itself are emphasized to simulate the ordered evolution trend of PMC project organizational management system and reveal the intrinsic causes of conflicts in PMC project and the key mechanisms of the PMC model application. The results show that first, the intensity of information communication between PMC subjects has a significant positive contribution to the orderliness of the organizational management system; second, too much acceleration of the project legal person's free will causes group chaos in the system, while too little slows down the group stabilization time, which has a negative impact on cost and schedule; third, the more the organizational structure of PMC contractors tends to the whole-process integrated control, the more it can drive the group to gather in an orderly manner and form a synergistic control mode combining self-organization and other organizations; and fourth, the implementation of the PMC model should focus on eliminating the traditional institutional and conceptual barriers, forming a project management model with integrated control of the whole process of the PMC project contractor and effective macro supervision of the project legal person. The research results of this paper revealed the intrinsic causes of conflicts in PMC projects and the key mechanisms of PMC model application; it can help solve the confrontational situation of PMC project participants, promote the development of the PMC model, and give full play to the investment benefits. [ABSTRACT FROM AUTHOR]

Aiming at the problem of pitch error of helical gear pair in engineering practice, the influence of pitch error on vibration, bifurcation, and chaos characteristics of the helical gear pair system is mainly studied. Due to the periodic time-varying nature of pitch error, a method of simulating the pitch error as a sine function is proposed to calculate pitch error. A nonlinear dynamic model of bending-torsion-shaft coupling of the helical gear pair system is established considering the effect of pitch error. The influence of pitch error on the vibration, bifurcation, and chaos characteristics of the system is analyzed by the Runge–Kutta numerical integration method. The research results show that the introduction of pitch error has the most significant impact on the torsional vibration of the system. With the increase in pitch error, the system exhibits rich bifurcation and chaos characteristics in the torsional direction. Moreover, it is also found that the vibration response in the torsional orientation of the system increases or decreases to the same degree when the system is in a periodic motion state, and the pitch error varies by the same extent. Therefore, the impact of pitch error on the dynamic performance of the helical gear pair system should be considered in engineering practice. [ABSTRACT FROM AUTHOR]

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period‐doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge‐based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long‐term chaotic behavior over a broad range of parameters. [ABSTRACT FROM AUTHOR]

This article summarizes the results of a numerical investigation of the phenomenon of escape in the N‐body ring configuration, focusing on the scenarios that result for N = 5, 6, 7, 8 peripheral bodies. There is a critical value of the Jacobi constant of the system such that for smaller values, the potential well opens and test particles may leave the potential through any of its N openings. By means of a surface of section, we show the results of the computation of the basins of escape towards the different directions of escape, analyzing the structures that appear in them. [ABSTRACT FROM AUTHOR]

Data mining is mostly utilized for a huge variety of applications in several fields like education, medical, surveillance, and industries. The clustering is an important method of data mining, in which data elements are divided into groups (clusters) to provide better quality data analysis. The Biogeography-Based Optimization (BO) is the latest metaheuristic approach, which is applied to resolve several complex optimization problems. Here, a Chaotic Biogeography-Based Optimization approach using Information Entropy (CBO-IE) is implemented to perform clustering over healthcare IoT datasets. The main objective of CBO-IE is to provide proficient and precise data point distribution in datasets by using Information Entropy concepts and to initialize the population by using chaos theory. Both Information Entropy and chaos theory are facilitated to improve the convergence speed of BO in global search area for selecting the cluster heads and cluster members more accurately. The CBO-IE is implemented to a MATLAB 2021a tool over eight healthcare IoT datasets, and the results illustrate the superior performance of CBO-IE based on F-Measure, intracluster distance, running time complexity, purity index, statistical analysis, root mean square error, accuracy, and standard deviation as compared to previous techniques of clustering like K-Means, GA, PSO, ALO, and BO approaches. [ABSTRACT FROM AUTHOR]

To describe and analyze the unstable periodic orbits of the Rucklidge system, a so-called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system are systematically investigated via a proposed variational method. The dynamics in the Rucklidge system are explored by using phase portrait analysis, Lyapunov exponents, and Poincaré first return maps. Symbolic encodings of the periodic orbits with two and four letters based on the trajectory topology in the phase space are implemented under two sets of parameter values. Meanwhile, the bifurcations of the periodic orbits are explored, significantly improving the understanding of the dynamics of the Rucklidge system. The multiple-letter symbolic encoding method could also be applicable to other nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stability of a stochastic delay system with impulsive signal is considered, and stability theorem of this system is proposed based on the Lyapunov–Razumikhin method; the convergence rate is also given, which gives theoretical foundation to chaos control and synchronization using the impulsive method. Finally, the classic delay chaos system with white noise and impulsive signal is employed to verify the feasibility and effectiveness of our theorem. [ABSTRACT FROM AUTHOR]

This paper constructs a supply chain model composed of a manufacturer and a recycler. The manufacturer's CSR and the recycler's fairness concerns are introduced to the benchmark model in turn, and the optimal decision-making problems under different models are studied and compared. The findings show that the manufacturer's utility will increase and the recycler's utility will decrease when the manufacturer undertakes CSR within a reasonable range. The optimal utility of manufacturers does not change, and the utility of the recycler is affected by the proportion of CSR undertaken by the manufacturer when the recycler considers fairness concerns. Based on the CSR and fairness model, this paper constructs a dynamic decision system of production quantity and eco-innovation effort. We analyze the influence of adjustment speed on the dynamic decision system and obtain the conditions required to maintain system stability. The research conclusion indicates that with the increase of adjusting parameters, the system gradually appears chaotic state from a stable state and the chaotic state of the system has a negative impact on the utility of manufacturer and recycler. In order to avoid chaos in the system, this paper uses the delayed feedback method to control the system. [ABSTRACT FROM AUTHOR]

Intensive and repetitive simulations are required to study static and dynamic behaviours of systems. Particular phenomena such as bifurcation and chaos require long simulation times and analysis. To check the existence of bifurcations and chaos in a dynamic system, a fine-tuning procedure of a bifurcation parameter is to be carried out. This increases considerably the computing time, and a great amount of patience is needed to obtain adequate results. Because of the high switching frequency of a boost inverter, the integration process of the dynamic model used to describe it uses an integration step that is in general less than one microsecond. This makes the integration process time consuming even for a short simulation. Thus, a fast, but accurate, method is suitable to analyse the dynamic behaviour of the converter. This work contains two topics. First, we develop a like-discrete integration process that permits precise results in a very fast manner. For one switching period, we compute only two or a maximum of three breaking points depending on whether we treat a continuous conduction mode (CCM) or a discontinuous conduction mode (DCM) of the inductor current. Furthermore, with each segment of the dynamic trajectory, an exact analytic formula is associated. The second goal is to use this result to develop a discrete iterative map formulated as in standard discrete time series models. The Jacobian matrix of the found iterative map is defined and used to compute Lyapunov exponents to prove existence of chaos. Performance of the developed study is positively evaluated by using classical simulations and fine-tuning a bifurcation parameter to detect chaos. This parameter is the desired reference of the inductor current peak. Results show that the proposed scheme is very fast and accurate. The study can be easily extended to other switching topologies of DC-DC inverters. [ABSTRACT FROM AUTHOR]

Machine learning is an expanding research area. Its main application is in the medical field and particularly the detection of epilepsy and epileptic seizures through electroencephalographic signals (EEG). It aims to design an intelligent framework that enables an immediate diagnosis of this disease without neurological consultation and thus saves the lives of the epileptic patients by detecting seizures and warning them before it happens. However, as a real-time application, this kind of framework faces several challenges such as accuracy, fast responses, and optimal memory usage. Within this context, our work was carried out. We propose a new machine learning framework based on chaos and fractal theories. Two main novelties are presented in this paper. Firstly, we propose a new method for signal preprocessing, and we reconstruct new versions of studied EEG signals using derivative determination and chaotic injection. Secondly, we suggest a new method for fractal analysis using Higuchi fractal dimension (HFD). In fact, HFDs extracted from EEG derivatives lead to detect epilepsy, whereas HFDs extracted from EEG with a chaotic signal injection lead to seizure detection. In addition, feature fusion helped to linearize all classification problems. An experimental study using the Bonn EEG database proves the efficiency of our contributions in comparison to published research. An accuracy of 100% was achieved in different classification cases using few features and a simple linear classifier. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behavior and control of chaotic systems with hidden attractors are studied. Firstly, a class of autonomous chaotic systems without the equilibrium point is proposed. Secondly, quantitative analysis methods are applied to explore the dynamic behavior of the new chaotic systems. Then, the Hamilton energy function of the new system is calculated by the Helmholtz theorem and the energy feedback controller is designed. Finally, the effectiveness of the controller is verified by numerical simulations. Compared with the line feedback control, the control effect of Hamilton energy control is better. [ABSTRACT FROM AUTHOR]

Nowadays, with a great number of household electrical appliances being discarded in every corner of the world every day, household electrical appliances recycling is attracting more attention. In this paper, we build a closed-loop supply chain that consists of a manufacturer and a third-party recycler based on the development of "Internet Plus" recovery platform. We thoroughly analyze the model and its evolution by chaos theory, complex dynamics theory, and numerical simulation and introduce the adaptive method to control the chaos of the system. We find that as the manufacturer increases the retail price, the stable area of the market becomes smaller. At the same time, when the manufacturers direct recycle price or the price adjustment range of the products recycled from the third party exceeds a certain threshold, all the recycle prices in the whole market will fluctuate, thus causing market chaos. Among them, as an adjustment decision method, delay strategy reduces the volatility of recycle price and makes it return to a stable state, which is an effective method to control system disorder. In addition, the third-party recycler will change the optimal subsidy model according to the government's price subsidy level, while the manufacturer always prefers the price subsidy model. [ABSTRACT FROM AUTHOR]

In order to facilitate lubrication and avoid the gear stuck due to thermal expansion, there needs to be a gap between the tooth profiles. As a strong nonlinear factor, the backlash will affect the motion state of the planetary gear system. When the gear failures occur, the motion state of the system will accordingly change. In this study, the meshing stiffness of the gear pair with tooth tip chipping fault is calculated by combining the analytic geometry method and the potential energy method. Then, a new nonlinear dynamic model including tooth backlash, time-varying mesh stiffness, and manufacturing error is established to study the dynamic response of the system. The equations of motion are derived by the Lagrangian method and solved by the numerical integration method. Taking the excitation frequency and tooth backlash as the variation parameters, respectively, the dynamic characteristics of the system are analyzed by comparing the global bifurcation diagrams between the health system and the fault system, and the path of the system into chaos is revealed. At the same time, the local characteristics of the system are revealed through the phase diagrams and Poincaré maps. The results show that with the variation of excitation frequency and tooth backlash, the fault system presents a more complex motion state. This study can provide the theoretical support for dynamic design and fault diagnosis of planetary gear transmission systems under the environment of gear fault-prone. [ABSTRACT FROM AUTHOR]

Image steganography has been widely adopted to protect confidential data. Researchers have been seeking to improve the steganographic techniques in order to increase the embedding capacity while preserving the stego-image quality. In this paper, we propose a steganography method using particle swarm optimization and chaos theory aiming at finding the best pixel locations in the cover image to hide the secret data while maintaining the quality of the resultant stego-image. To enhance the embedding capacity, the host and secret images are divided into blocks and each block stores an appropriate amount of secret bits. Experimental results show that the proposed scheme outperforms existing methods in terms of the PSNR and SSIM image quality metrics. [ABSTRACT FROM AUTHOR]

Due to the growing of the use of Internet and communication media, image encryption is rapidly increased. Image sharing through unsafe open channels is vulnerable for attacking and stealing. For protecting the images from attacks, encryption techniques are required. Recently, new and efficient chaos-based techniques have been suggested to develop secure image encryption. This study presents a novel image encryption framework based on integrating the chaotic maps and color codes. Three phases are involved in the proposed image encryption technique. Piecewise chaotic linear map (PWLCM) is used in the first phase for permuting the digital image. In the second phase, substitution is done using Hill cipher which is the mixing of color codes with the permuted image. The third phase is implemented by XORing, a sequence generated by the chaotic logistic map (CLM). The proposed approach enhances the diffusion ability of the image encryption making the encrypted images resistant to the statistical differential attacks. The results of several analyses such as information entropy, histogram correlation of adjacent pixels, unified average changing intensity (UACI), number of pixel change rate (NPCR), and peak signal-to-noise ratio (PSNR) guarantee the security and robustness of the proposed algorithm. The measurements show that the proposed algorithm is a noble overall solution for image encryption. Thorough comparison with other image encryption algorithms is also carried out. [ABSTRACT FROM AUTHOR]

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic and periodic behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied. [ABSTRACT FROM AUTHOR]

Chaos in piezoelectric composite laminated beams has significant implications in the design of this model. Some results for this model have been obtained numerically. With the energy-phase method and numerical simulations, global dynamics of piezoelectric composite laminated beams is investigated in this paper. The average equation of the piezoelectric composite laminated beam is obtained by the normal form theory. The existence of multipulse homoclinic orbits for undisturbed and dissipative cases is analyzed by the energy-phase method, and the mechanism of chaotic motion of the system is given. The effect of the dissipation factor on pulse sequence and layer radius is studied in detail. The chaotic motion of the system is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

Based on the existing financial system risk models, a set of time-lag financial system risk models is established considering the influence brought by time-lag factors on the financial risk system, and the dynamical behavior of this system is analyzed by using chaos theory. Through Matlab simulation, the bifurcation diagram and phase diagram of time-lag risk intensity and control intensity are plotted. The analysis shows that this kind of time-lag financial system risk model has complex dynamic behavior, different motion states will appear when different parameter values are selected, and the time-lag risk intensity parameter also has a very strong influence on the system motion. To ensure the operation of the financial system in a stable state, measures with certain delay effects must be taken to control the risk and to choose the appropriate time-lag control intensity, and too much or too little time-lag control intensity is not conducive to the benign operation of the system. [ABSTRACT FROM AUTHOR]

In recent years, the research of chaos theory has developed from simple cognition and analysis to practical engineering application. In particular, hyperchaotic systems with more complex and changeable chaotic characteristics are more sensitive and unpredictable, so they are widely used in more fields. In this paper, two important engineering applications based on hyperchaos pseudorandom number generator (PRNG) and image encryption are studied. Firstly, the coupling 6D memristive hyperchaotic system and a 2D SF-SIMM discrete hyperchaotic mapping are used as the double entropy source structure. The double entropy source structure can realize a new PRNG that meets the security requirements, which can pass the NIST statistical test when the XOR postprocessing method is used. Secondly, based on the double entropy source structure, a new image encryption algorithm is proposed. The algorithm uses the diffusion-scrambling-diffusion encryption scheme to realize the conversion from the original plaintext image to the ciphertext image. Finally, we analyze the security of the proposed PRNG and image encryption mechanism, respectively. The results show that the proposed PRNG has good statistical output characteristics and the proposed image encryption scheme has high security, so they can be effectively applied in the field of information security and encryption system. [ABSTRACT FROM AUTHOR]

Zero-watermarking is one of the solutions for image copyright protection without tampering with images, and thus it is suitable for medical images, which commonly do not allow any distortion. Moment-based zero-watermarking is robust against both image processing and geometric attacks, but the discrimination of watermarks is often ignored by researchers, resulting in the high possibility that host images and fake host images cannot be distinguished by verifier. To this end, this paper proposes a PCET- (polar complex exponential transform-) based zero-watermarking scheme based on the stability of the relationships between moment magnitudes of the same order and stability of the relationships between moment magnitudes of the same repetition, which can handle multiple medical images simultaneously. The scheme first calculates the PCET moment magnitudes for each image in an image group. Then, the magnitudes of the same order and the magnitudes of the same repetition are compared to obtain the content-related features. All the image features are added together to obtain the features for the image group. Finally, the scheme extracts a robust feature vector with the chaos system and takes the bitwise XOR of the robust feature and a scrambled watermark to generate a zero-watermark. The scheme produces robust features with both resistance to various attacks and low similarity among different images. In addition, the one-to-many mapping between magnitudes and robust feature bits reduces the number of moments involved, which not only reduces the computation time but also further improves the robustness. The experimental results show that the proposed scheme meets the performance requirements of zero-watermarking on the robustness, discrimination, and capacity, and it outperforms the state-of-the-art methods in terms of robustness, discrimination, and computational time under the same payloads. [ABSTRACT FROM AUTHOR]