Behavior Of Nonlinear Systems Research Articles

DYNAMICS OF OPTICAL WAVE PROFILES TO THE FRACTIONAL THREE-COMPONENT COUPLED NONLINEAR SCHRÖDINGER EQUATION

This paper explores the truncated [Formula: see text]-fractional three-component coupled nonlinear Schrödinger (tc-CNLS) equation, that regulates the behavior of optical pulses in optical fibers. These equations are utilized in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. The study of multi-component NLS equations has gained significant attention due to their ability to elucidate various complex physical phenomena and exhibit more dynamic structures of localized wave solutions. The freshly invented integration tools, known as the fractional modified Sardar subequation method (MSSEM) and fractional enhanced modified extended tanh-expansion method (eMETEM), are employed to ensure the solutions. The study focuses on extracting various types of optical solitons, including bright, dark, singular, bright-dark, complex, and combined solitons. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. The utilized methodology is effective in explaining fractional nonlinear partial differential equations (FNLPDEs) as it offers pre-existing solutions and additionally derives novel exact solutions by mixing outcomes from various procedures. Furthermore, we plot the visualizations of solutions by plotting 3D, 2D, and contour graphs with the corresponding parameter values. The findings of this paper can improve the understanding of the nonlinear dynamical behavior of a specific system and demonstrate the efficacy of the methodology used. We anticipate that our study will provide substantial benefits to a considerable group of engineering model experts. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

Lump and kink soliton phenomena of Vakhnenko equation

Understanding natural processes often involves intricate nonlinear dynamics. Nonlinear evolution equations are crucial for examining the behavior and possible solutions of specific nonlinear systems. The Vakhnenko equation is a typical example, considering that this equation demonstrates kink and lump soliton solutions. These solitons are possible waves with several intriguing features and have been characterized in other naturalistic nonlinear systems. The solution of nonlinear equations demands advanced analytical techniques. This work ultimately sought to find and study the kink and lump soliton solutions using the Riccati–Bernoulli sub-ode method for the Vakhnenko equation (VE). The results obtained in this work are lump and kink soliton solutions presented in hyperbolic trigonometric and rational functions. This work reveals the effectiveness and future of our method for solving complex solitary wave problems.

The fusion of quantum chaos and nonlinear dynamics in securing image encryption

In the rapidly evolving landscape of digital communication, the security of image data transmits paramount importance. This paper introduces a novel encryption framework that integrates the principles of quantum chaos and nonlinear dynamics to fortify image encryption processes. Recognizing the vulnerabilities inherent in conventional encryption methods, our research seeks to harness the unpredictable nature of quantum chaos alongside the complex behavior of nonlinear dynamical systems to generate robust encryption keys that are highly sensitive to initial conditions. Utilizing a mathematical model that combines the unpredictability of quantum chaotic systems with the intricate patterns of nonlinear dynamics, we develop an encryption algorithm that demonstrates superior resistance to both brute-force attacks and statistical analysis. The algorithm’s efficacy is evaluated through a series of rigorous tests, including entropy analysis, correlation coefficient assessment, and resistance to known-plaintext and chosen-plaintext attacks.

Coupling dynamics of pedestal looseness and impact-rub for rotor system with nonlinear support

It is easy for the rotor system to produce the plastic deformation at the support after a long-term operation, this change will cause looseness of the bolt. Due to the particularity of the material and the structure for the bearing base and foundation, the elastic force of the support is nonlinear. Larger vibration of the loosening rotor under the nonlinear support will occur, resulting in the impact-rub between the rotor and stator. In order to study the dynamic behaviors of the loosening-rubbing coupling rotor system under the nonlinear support, the model is established to analyze the influencing mechanism of the key parameters such as the eccentricity, the disk offset, the looseness gap, the rubbing gap, and the nonlinear parameters on the vibrational responses of the system. The piecewise cubic nonlinear expression is applied to describe the nonlinear support with the loosing bolt; Coulomb friction is employed to characterize the rubbing of the impact-rub. The research results show that the nonlinear support will stimulate and amplify the nonlinear dynamic behaviors of the rotor system; there exists a threshold for the effect of the loosening gap on the vibrational characteristics of the system; increasing nonlinear parameters to a certain degree will cause the increase of the proportion of quasi-period and chaos. The research focus and conclusions are certain innovative in this paper. The work is of great value for fault diagnosis and structural design.

Comparative Analysis of Nonlinear Dynamics of an Angular Velocity System of 2-DOF Aerial Manipulator with Different Physical Parameters

The two-degree-of-freedom (2-DOF) aerial manipulator is composed of a quadrotor aircraft and a 2-DOF manipulator, which significantly expands the scope of grabbing and transporting objects. After the manipulator is installed on the quadrotor, the manipulator and the load will cause serious interference to the quadrotor, resulting in difficulty of system control and even instability. This paper presents a mathematical model of the angular velocity system of the 2-DOF aerial manipulator. The model considers the influence of the manipulator and the load on the quadrotor. Based on this model, the nonlinear dynamics of the angular velocity system of the 2-DOF aerial manipulator are analyzed by solving the equilibrium points, calculating the Lyapunov exponents, analyzing the dynamic bifurcation diagram, and drawing the dynamic region distribution map. It is found that angular velocity can produce the dynamic behaviors of sink, period-doubling, and chaos under certain circumstances. By analyzing the nonlinear dynamic behaviors of the angular velocity system under different manipulator postures, different manipulator configurations, different load masses, and different load resistances, the stability of the angular velocity system is analyzed to guide the use of the aerial manipulator more safely and efficiently.

Analysis of bifurcation, chaotic structures, lump and $ M-W $-shape soliton solutions to $ (2+1) $ complex modified Korteweg-de-Vries system

<abstract><p>This research focuses on the fascinating exploration of the $ (2+1) $-dimensional complex modified Korteweg-de Vries (CmKdV) system, exhibiting its complex dynamics and solitary wave solutions. This system is a versatile mathematical model that finds applications in various branches of physics, including fluid dynamics, plasma physics, optics, and nonlinear dynamics. Two newly developed methodologies, namely the auxiliary equation (AE) method and the Hirota bilinear (HB) method, are implemented for the construction of novel solitons in various formats. Numerous novel soliton solutions are synthesised in distinct formats, such as dark, bright, singular, periodic, combo, $ W $-shape, mixed trigonometric, exponential, hyperbolic, and rational, based on the proposed methods. Furthermore, we also find some lump solutions, including the periodic cross rational wave, the homoclinic breather (HB) wave solution, the periodic wave solution, the $ M $-shaped rational wave solution, the $ M $-shaped interaction with one kink wave, and the multiwave solution, which are not documented in the literature. In addition, we employ the Galilean transformation to derive the dynamic framework for the presented equation. Our inquiry includes a wide range of topics, including bifurcations, chaotic flows, and other intriguing dynamic properties. Also, for the physical demonstration of the acquired solutions, 3D, 2D, and contour plots are provided. The resulting structure of the acquired results can enrich the nonlinear dynamical behaviors of the given system and may be useful in many domains, such as mathematical physics and fluid dynamics, as well as demonstrate that the approaches used are effective and worthy of validation.</p></abstract>

Seismic performance of confined prestressed hollow core wall panels part II: Numerical simulation and analysis

In Part I of this research, confined prestressed hollow core wall structures were proposed and experimental tests of 19 specimens were conducted to study its mechanical behaviors. In this part, a detailed finite element model was developed in ANSYS to provide a tool for further investigating the seismic behaviors of confined prestressed hollow core wall structures. Contact elements were applied to simulate the interaction between material interfaces. Techniques in ANSYS including coupling of degrees of freedom (CP) of overlapped nodes and deactivation of concrete elements (EKILL) were adopted, along with restart analysis (REST) to simulate nonlinear mechanical behaviors of the structural system. The developed modeling method was verified by the experimental test results and was shown to accurately predict the global and local behaviors such as failure modes and load bearing capacities of precast hollow core walls. Parametric analysis on shear span ratio, axial load ratio, rigidity of floor systems as well as strength of vertical wall-wall joints was conducted, and relevant design recommendations were provided for prestressed hollow core wall structures. Results show that for a ductile prestressed hollow core wall structure, the axial load ratio is recommended to be smaller than 0.06 and the story number less than 5. Influence of rigidity of floor systems requires further study with dynamic tests, but low-strength vertical wall-wall joint is highly recommended for this system. Two analytical mechanisms that are shear-flexural mechanism and truss mechanism were proposed for calculation of load bearing capacities. These two mechanisms provide good predictions for an upper bound and a lower bound for load bearing capacities of prestressed hollow core walls, respectively. From Part I and II of this research, the mechanical behaviors of prestressed hollow core wall structures are verified experimentally, numerically, and theoretically, and it is concluded that they can be used as a potential choice for low-rise buildings in rural areas.

Machine Learning Approaches for Predicting Chaotic Behavior in Nonlinear Systems

Machine Learning Approaches for Predicting Chaotic Behavior in Nonlinear Systems

Dynamic Analysis and Suppression Strategy Research on a Novel Fractional-Order Ferroresonance System

Ferroresonance is characterized by overvoltage and irregular operation in power systems, which can greatly endanger system equipment. Mechanism analysis of the ferroresonance phenomenon depends mainly on model accuracy. Due to the fractional-order characteristics of capacitance and inductance, fractional-order models are more universal and accurate than integer-order models. A typical 110 kV ferroresonance model is first established. The influence of the excitation amplitude on the dynamic behavior is analyzed. The fractional-order ferroresonance model is then introduced, and the effects of the fractional order and flux-chain order on the system’s motion state are studied via bifurcation diagrams and phase portraits. In order to suppress the nonlinear dynamic behavior of fractional-order ferroresonance systems, a novel fractional-order fast terminal sliding mode control method based on finite-time theory and the frequency distributed model is proposed. A new fractional-order sliding mode surface and control law using a saturation function are developed. A robust fractional-order sliding mode controller could achieve finite-time stabilization and tracking despite model uncertainties and external disturbances. Compared with conventional sliding mode methods, the simulation results highlight the effectiveness and superiority. The research provides a theoretical basis for ferroresonant analysis and suppression in large-scale interconnected power grids.

High geometric fidelity through closed-loop control of the weld pool size in gas metal arc welding based direct energy deposition

Arc based direct energy deposition combines the flexibility of additive manufacturing with high build rates and low investment costs. However, high geometric fidelity of manufactured components is not possible with state-of-the-art methods. Highly varying and geometry-dependent boundary conditions, e.g. heat dissipation and the interpass temperature, are quasi-random influences with a strong impact on the geometric fidelity and the manufactured microstructure. Without adjusting for these variations, process stability decreases, geometric deviations become more likely and defects accumulate from layer to layer. A high geometric fidelity of the manufactured components can therefore not be guaranteed with the state of the art. Due to the large number of influencing variables in the arc-based manufacturing process, this problem cannot be solved by the definition of simple setpoints. Closed-loop control, however, offers the opportunity to flexibly counteract any deviations that occur by adjusting the process parameters in real time. Since the manufactured part is created by solidification from the weld pool, a closed-loop control of the weld pool size is being developed. The developed controller uses the weld pool properties and the interpass temperature as feedback variables and takes into account the non-linear system behaviour as well as the process noise and the parameter uncertainties. The subordinate control of the welding power source is further used for improved process stability. To the best of our knowledge, this solution provides a level of robustness, steady-state accuracy and geometric fidelity that has not been achieved by previous approaches reported in the literature. To illustrate the performance of this closed-loop control for components with low heat dissipation, we demonstrate the fabrication of thin-walled components with high geometric accuracy for a fast 3D printing process and investigate the influence of the welding process variables on the microstructure, the evaluation of the geometric fidelity is based on EN ISO 1101.

The Efficiency of Using Machine Learning Techniques in Fiber-Reinforced-Polymer Applications in Structural Engineering

Sustainable solutions in the building construction industry have emerged as a new method for retrofitting applications in the last two decades. Fiber-reinforced polymers (FRPs) have garnered much attention among researchers for improving reinforced concrete (RC) structures. The existing design guidelines for FRP-strengthened RC members were developed using empirical methods that are based on specific databases, limiting the accuracy of the predicted results. Therefore, the use of innovative and efficient prediction tools to predict the behavior of FRP-strengthened RC members has become essential. During the last few years, efforts have been progressively focused on the use of machine learning (ML) as a feasible and effective technique for solving various structural engineering problems. Its capability to predict the behavior of complex nonlinear structural systems while considering a wide range of parameters offers a distinctive opportunity to make the behavior of RC members more predictable and accurate. This paper aims to evaluate the current state of using various ML algorithms in RC members strengthened with FRP to enable researchers to determine the capabilities of current solutions as well as to find research gaps to carry out more research to bridge revealed knowledge and practice gaps. Scopus databases were searched using predefined standards. The search revealed ninety-six articles published between 2016 and 2023. Consequently, these articles were analyzed for ML applications in the field of FRP retrofitting, including flexural and shear strengthening of RC beams, flexural strengthening of slabs, confinement and compressive strength of columns, and FRP bond strength. The results reveal that 32% of the reviewed studies focused on the application of ML techniques to the flexural and shear strengthening of RC beams, 32% on the confinement and compressive strength of columns, 6.5% on the flexural strengthening of slabs, 22% on FRP bond strength, 6.5% on materials, and 1% on beam–column joints. This research also revealed that the application of various ML algorithms has shown a significant improvement in resistance prediction accuracy as compared with the existing empirical solutions. Supervised learning techniques were the most favorable learning method due to their good generalization, interpretability, adaptability, and predictive efficiency. In addition, the selection of suitable ML algorithms and optimization techniques is found to be mainly dictated by the nature of the problem and the characteristics of the dataset. Nonetheless, selecting the most appropriate ML model and optimization algorithm for each specific application remains a challenge, given that each algorithm is developed with different principles and methodologies.

Stability for nonlinear delay systems: Self-triggered impulsive control

This paper studies the stability problem of nonlinear delay systems in the framework of self-triggered impulsive control (STIC), where a class of self-triggered mechanisms is designed based on comparison approach. Different from the traditional event-triggered impulsive control (ETIC), in this paper the next impulse instant can be predicted at the previous impulse instant, and there is no need for state monitoring between two adjacent impulse instants. Under the proposed STIC strategy, some sufficient conditions for non-Zeno behavior and asymptotical stability of nonlinear delay systems are presented, respectively. Finally, two numerical examples are carried out to illustrate the effectiveness of the theoretical results.

Interval multiobserver for feedback control of discrete time nonlinear systems

In this paper, an interval multiobserver is designed for nonlinear systems subject to unknown but bounded disturbances and measurement noises. The behavior of discrete nonlinear systems is described by an uncoupled multimodel. Linear Matrix Inequalities (LMIs) are formulated to study the stability of the proposed systems and to ensure the cooperativity dynamic of the observation errors. An augmented system is introduced to apply a tracking control where the control gains are obtained by pole placement. Finally, a numerical example is proposed to verify the efficiency of the interval multiobserver in state estimation and to prove the performance of the control strategy to follow the desired trajectory.

Dynamic simulation and projection of land use change using system dynamics model in the Chinese Tianshan mountainous region, central Asia

A critical step in alleviating the contradiction between human activities and land systems is to project and analyze land use change traits in various scenarios to furnish a basis for formulating economic development and ecological conservation strategies. However, few studies have examined land use change using the system dynamics (SD) model and patch-generating land use simulation (PLUS) model in the Chinese Tianshan mountainous region (CTMR) affected by different economic growth patterns and climate change contexts. Therefore, based on the Shared Socioeconomic Pathways and Representative Concentration Pathways (SSPs-RCPs) scenarios, we attempted to construct a regional SD model (RSDM) including population, economic, land, and climate subsystems. Then, the coupled model by combining RSDM and PLUS was employed to simulate and project land use/cover changes (LUCC) in the CTMR at the regional level to explore the spatial distribution of land and its pattern of change in different climate contexts. The SD model is an effective method that can simulate the nonlinear behavior of a complex system and predict its evolution through the interactions and feedback relationships between different influencing factors. The PLUS model is an effective tool that can be used to simulate the evolution of land patches and capture the extent to which the driving factors contribute to LUCC. The relative errors were less than 5%, and the total accuracy of PLUS model was 91.77%. The above results demonstrated the effectiveness of RSDM and PLUS model in modeling LUCC across the CTMR. From 2005 to 2020, there was an expansion trend in the area of forest and construction land as well as in the area of cultivated land, while the grassland area displayed a significant decline. By 2040, the area of unused land, grassland, and water is expected to demonstrate a decreasing trend while other land types increase, with construction land showing the most significant increase of 101.37% under the SSP585 scenario. It is anticipated to expand mainly to cultivated land and grassland around cities. The cultivated land is expected to primarily encroach on the regions of unused land and grassland under the three scenarios, reaching the expansion demand. As opposed to the scenarios of SSP126 and SSP245, the SSP585 scenario distribution of the cultivated land patches will be more compact and denser. The SSP126 and SSP245 scenarios will exhibit similar patterns of future spatial distribution of land. The SSP585 scenario is anticipated to display marked differences. According to the three scenarios, grassland degradation will be severe and require increased grassland protection. The findings can offer novel perspective concepts with regard to future ecological and environmental management, judicious distribution of land resources, and sustainable progression in the CTMR.

A Hybrid Renewable Sources Implementation for a DC Microgrid with Flatness-Nonlinear Control to Achieve Efficient Energy Management Strategy

The significance of energy management using sustainable energy sources and the merits of DC in AC microgrids are due to less complexity, smaller size, and fewer conversion stages. In this paper, we propose a standard-islanded DC microgrid with photovoltaic (PV) and fuel cell (FC) primary sources and a supercapacitor (SC) storage unit. The proposed system provides high-quality energy supplied to the DC load under different levels of solar irradiation and changing loading situations. Taking into account the slow dynamic response of the FC, the SC provides transient periods under various conditions to maintain stability of the system. Because of the nonlinear system's behavior, differential flatness-based control has been applied mainly in nonlinear systems where the number of variables to the outputs is reduced with a robust control system established through inherited parameter reductions and equality constraints due to the system trajectories (x, u) is straightforwardly estimated from flat output trajectories y and their derivatives without any differential equation integration. The PI control is executed when the SC adjusts the DC bus voltage variation. Therefore, the objective is to provide management that ensures stable DC bus voltage and arranges power sharing between variable sources and power balance with a load. Flatness PI has been investigated and has proven effective in offering faster response without overshoot and greater robustness.

Dynamical and physical characteristics of soliton solutions to the (2+1)-dimensional Konopelchenko–Dubrovsky system

Abstract Soliton solutions of the Konopelchenko–Dubrovsky (KD) equation using four analytical methods are established. The KD system is used to study the portrays in physics with weak dispersion. The investigated results are obtained in different forms such as trigonometric, hyperbolic, and exponential functions. For the physical behavior of the concerned nonlinear system, some solutions are plotted graphically via assigning the certain values to the parameters. Mathematica software 11.11 is used to handle all results as well as figures. Hence, searched results have rewarding recompenses in nonlinear science.

On the undesired equilibria induced by control barrier function based quadratic programs

In this paper, we analyze the system behavior for general nonlinear control-affine systems when a control barrier function-induced quadratic program-based controller is employed for feedback. In particular, we characterize the existence and locations of possible equilibrium points of the closed-loop system and also provide analytical results on how design parameters affect them. Based on this analysis, a simple modification on the existing quadratic program-based controller is provided, which, without any assumptions other than those taken in the original program, inherits the safety set forward invariance property, and further guarantees the complete elimination of undesired equilibrium points in the interior of the safety set as well as one type of boundary equilibrium points, and local asymptotic stability of the origin. Numerical examples are given alongside the theoretical discussions.

Optimal auxiliary function method for analyzing nonlinear system of coupled Schrödinger–KdV equation with Caputo operator

Abstract The optimal auxiliary function method (OAFM) is introduced and used in the analysis of a nonlinear system containing coupled Schrödinger–KdV equations, all within the framework of the Caputo operator. The OAFM, known for its efficiency in solving nonlinear issues, is used to obtain approximate solutions for the coupled equations’ complicated dynamics. Numerical and graphical assessments prove the suggested method’s correctness and efficiency. This study contributes to the understanding and analysis of coupled Schrödinger–KdV equations and their many applications by providing insights into the behavior of nonlinear systems within mathematical physics.

Performance Analysis of a Backward/Forward Algorithm Adjusted to a Distribution Network with Nonlinear Loads and a Photovoltaic System

Context: The backward/forward (BF) algorithm is a sweep-type technique that has recently been used as a strategy for the power flow analysis of ill-conditioned networks. The purpose of this study is to evaluate the performance of the BF algorithm compared to that of a computational tool such as Simulink, with both strategies adjusted to the operating conditions of a distribution network with nonlinear components (loads and photovoltaic system), unbalanced loads, and harmonic distortion in the voltage and current signals. Method: The study case is a low-voltage distribution network with a radial topology, unbalanced loads, and nonlinear components. The BF algorithm is adjusted to consider two approaches of the Norton model: a coupled admittance matrix and a decoupled admittance matrix. The latter is also used in the network model created in Simulink. The performance of the algorithm is evaluated by analyzing 18 operation scenarios defined according to the presence and use intensity of the loads and solar irradiance levels (low and high). Results: In general, the three strategies could successfully determine the waveform and RMS values of the voltage signals with errors of less than 0,8 and 1,3%, respectively. However, the performance of the strategies for the estimation of current signals and power parameters shows errors of 5-300% depending on the level of solar irradiance at which the photovoltaic system operates. Conclusions: The results show that the BF strategy can be used to analyze unbalanced power grids with increasing penetration of renewable generation and the integration of nonlinear devices, but the performance of this strategy depends on the load model applied to represent the behavior of nonlinear devices and generation systems.

Nonlinear dynamics and chaos control of circular dielectric energy generator

The current study focuses on the nonlinear dynamics of the dielectric elastomer generator (DEG). To begin with, we will go through DEG’s operating principles, parameters, materials, and deformation modes. On this basis, the dynamical modeling for the nonlinear behavior of the DEG system is described, and the second-order nonlinear ordinary differential equation representing radially symmetric motion is derived using Hamilton’s variational principle. A static applied electric field allows the DEG system to attain two equilibrium states: thick and thin. The effects of the stiffening phenomenon on the dynamics of the DEG system are investigated. The system converges to a stable equilibrium point under constant loads, and the convergence position and velocity are closely related to both the initial states. Subjected to periodic loads, certain phenomena such as quasiperiodicity and chaos are detected, and the chaotic phenomena are explored using the bifurcation diagram and 0-1 chaos test. Furthermore, parametric studies are carried out using numerical analyses to demonstrate the influence of load amplitude and external frequency on the dynamics of the DEG system. Once the DEG enters the chaotic regime, the chaotic zone is transformed into a stable manifold using established chaos control techniques such as system parameter change and parametric perturbation. However, because these techniques require changes in system design, we proposed a chaos control by using a non-linear controller, specifically, adaptive integral backstepping sliding mode control (AIBSMC) as one demonstrative candidate. The controller also enables the DEG system to follow motion along a predefined trajectory. The current work may be expected to substantially impact the future design and performance of energy harvesters.