Nonlinear Dynamics Research Articles

Learning-based Control for Deployment and Retrieval of a Spinning Tethered Satellite Formation System

This paper investigates the nonlinear dynamics and control of the deployment and retrieval for a spinning tethered satellite formation system via artificial intelligent method. A dynamic model of the spinning tethered formation system is developed to describe the attitude motions of the system, involving the relative rotations of the tethers to the central main satellite. Considering the system with symmetric and asymmetric configurations, a learning-based control strategy with low time cost is proposed to achieve the stable deployment and retrieval of tethers. In the strategy, a nonlinear model predictive control law accounting for the control constraints and nonlinear dynamics is developed to achieve the control goal. Based on a deep learning method, a dataset including control input and state output obtained offline is trained to form deep neural networks. An online feedback control of the system can be achieved by conducting real-time mapping from the system state to the control input using the neural networks. Finally, numerical simulations for deployment and retrieval of the system with different configurations are presented to demonstrate the computational efficiency and to validate the effectiveness of the control strategy.

Simplified internal models in human control of complex objects

Humans are skillful at manipulating objects that possess nonlinear underactuated dynamics, such as clothes or containers filled with liquids. Several studies suggested that humans implement a predictive model-based strategy to control such objects. However, these studies only considered unconstrained reaching without any object involved or, at most, linear mass-spring systems with relatively simple dynamics. It is not clear what internal model humans develop of more complex objects, and what level of granularity is represented. To answer these questions, this study examined a task where participants physically interacted with a nonlinear underactuated system mimicking a cup of sloshing coffee: a cup with a ball rolling inside. The cup and ball were simulated in a virtual environment and subjects interacted with the system via a haptic robotic interface. Participants were instructed to move the system and arrive at a target region with both cup and ball at rest, ’zeroing out’ residual oscillations of the ball. This challenging task affords a solution known as ‘input shaping’, whereby a series of pulses moves the dynamic object to the target leaving no residual oscillations. Since the timing and amplitude of these pulses depend on the controller’s internal model of the object, input shaping served as a tool to identify the subjects’ internal representation of the cup-and-ball. Five simulations with different internal models were compared against the human data. Results showed that the features in the data were correctly predicted by a simple internal model that represented the cup-and-ball as a single rigid mass coupled to the hand impedance. These findings provide evidence that humans use simplified internal models along with mechanical impedance to manipulate complex objects.

Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: an iterative framework for nonlinear wave dynamics

Abstract This paper addresses the solution of the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation using the Conformable Laplace Decomposition Method (CLDM). The CDGSK equation, a fundamental model in wave dynamics and fluid mechanics, is explored for its applications in quantum mechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractional derivatives influence the physical characteristics of wave propagation in both optical and quantum systems. The exact solutions obtained provide insight into soliton behavior, essential for understanding wave-particle interactions in quantum fields and light–matter interactions in optics. The fractional nature of the equation allows for more accurate modeling of non-integer order dynamics commonly found in optical fibers and quantum waveguides. The CLDM method proves to be highly effective, providing approximate solutions with minimal computational effort. These findings offer significant contributions to the fields of quantum mechanics and nonlinear optics, where the fractional CDGSK equation can be applied to solve complex wave equations with great accuracy.

Non-Hermitian Global Synchronization.

Synchronization of coupled nonlinear oscillators is a prevalent phenomenon in natural systems and can play important roles in various fields of modern science, such as laser arrays and electric networks. However, achieving robust global synchronization has always been a significant challenge due to its extreme susceptibility to initial conditions and structural perturbations. Here, a novel approach is presented to achieve robust global synchronization by manipulating the interplay between non-Hermitian physics and nonlinear dynamics. Remarkably, the initial-state-independent non-Hermitian skin and topological global synchronization are proposed, exhibiting diverse anomalous effects such as the enlarged-size triggered non-Hermitian global synchronization and nonlinear skin states-dominated global synchronization. To validate the findings, nonlinear topoelectrical circuits for experimental observation of non-Hermitian global synchronization are designed and fabricated. The work opens up a promising avenue for establishing resilient global synchronization with potential applications in constructing high-radiance laser arrays and topologically synchronized networks.

PID control algorithm based on multistrategy enhanced dung beetle optimizer and back propagation neural network for DC motor control.

Traditional Proportional-Integral-Derivative (PID) control systems often encounter challenges related to nonlinearity and time-variability. Original dung beetle optimizer (DBO) offers fast convergence and strong local exploitation capabilities. However, they are limited by poor exploration capabilities, imbalance between exploration and exploitation phases, and insufficient precision in global search. This paper proposes a novel adaptive PID control algorithm based on enhanced dung beetle optimizer (EDBO) and back propagation neural network (BPNN). Firstly, the diversity of exploration is increased by incorporating a merit-oriented mechanism into the rolling behavior. Then, a sine learning factor is introduced to balance the global exploration and local exploitation capabilities. Additionally, a dynamic spiral search strategy and adaptive [Formula: see text]-distribution disturbance are presented to enhance search precision and global search capability. The BPNN is employed to fine-tune both PID and network parameters, leveraging its powerful generalization and learning ability to model nonlinear system dynamics. In the simplified motor experiments, the proposed controller achieved the lowest overshoot (0.5%) and the shortest response time (0.012s), with a settling time of 0.02s and a steady-state error of just 0.0010. In another set of experiments, the proposed controller recorded an overshoot and response time of 0.7% and 0.0010s, across five DC motor tests. These results demonstrate the proposed adaptive PID control algorithm has superior performance in optimizing control system parameters, as well as improving system robustness and stability.

Analytical solutions of the Caudrey-Dodd-Gibbon equation using Khater II and variational iteration methods.

This study focuses on solving the Caudrey-Dodd-Gibbon ( ) equation using the Khater II ( ) method and the Variational Iteration ( ) method. The equation is a pivotal mathematical model in nonlinear wave dynamics, essential for understanding the evolution, interaction, and preservation of wave forms in dispersive media. Its applications span various fields, including fluid dynamics, nonlinear optics, and plasma physics, where it plays a crucial role in analyzing solitons and complex wave interactions. In this research, we meticulously implement the and methods to derive solutions for this nonlinear partial differential equation. Our findings reveal new aspects of the equation's behavior, offering deeper insights into nonlinear wave phenomena. The significance of this study lies in its contribution to advancing the understanding of these phenomena and their practical applications in the academic realm. The results underscore the effectiveness of the employed methods, their innovative contributions, and their relevance to applied mathematics.

A Hybrid Approach of Substitution and Permutation techniques for Modern Image-Cryptosystem

Abstract This paper proposes a new image encryption algorithm based on the introduction of cellular automata with Galois field-based methods to further encourage a higher level of security. This begins the encryption process by creating an initial substitution box from the irreducible polynomials in the Galois field, followed by the final substitution box obtained through permutation operations. This lays
the foundation for a sound cryptographic process. In order to handle different cryptographic attack types, balance in the substitution box has been closely analyzed. Additionally, we leverage the chaotic nature of the logistic map to incorporate a random element, significantly strengthening the encryption scheme against diverse cryptanalytic attacks. Nonlinear dynamics, as introduced by cellular automata, further develop the encryption process and disperse the image’s data, making it more intricate for any potential attacker. The differential analysis validates the encryption scheme’s resistance to differential attacks, thereby confirming its potential for secure image transmission and storage. The proposed hybrid approach presents a comprehensive solution for image encryption, ensuring high security and computational efficiency. This contribution is an added advantage in the development of image cryptosystems,
addressing the modern challenges facing secure data within the digital landscape.

Learning extreme vegetation response to climate drivers with recurrent neural networks

Abstract. The spectral signatures of vegetation are indicative of ecosystem states and health. Spectral indices used to monitor vegetation are characterized by long-term trends, seasonal fluctuations, and responses to weather anomalies. This study investigates the potential of neural networks in learning and predicting vegetation response, including extreme behavior from meteorological data. While machine learning methods, particularly neural networks, have significantly advanced in modeling nonlinear dynamics, it has become standard practice to approach the problem using recurrent architectures capable of capturing nonlinear effects and accommodating both long- and short-term memory. We compare four recurrent-based learning models, which differ in their training and architecture for predicting spectral indices at different forest sites in Europe: (1) recurrent neural networks (RNNs), (2) long short-term memory networks (LSTMs), (3) gated recurrent unit networks (GRUs), and (4) echo state networks (ESNs). While our results show minimal quantitative differences in their performances, ESNs exhibit slightly superior results across various metrics. Overall, we show that recurrent network architectures prove generally suitable for vegetation state prediction yet exhibit limitations under extreme conditions. This study highlights the potential of recurrent network architectures for vegetation state prediction, emphasizing the need for further research to address limitations in modeling extreme conditions within ecosystem dynamics.

Advanced hybrid control for induction motor combining ANN-PID speed controller with neural predictive current regulator based on particle swarm optimization

This paper presents a hybrid control strategy for an induction motor (IM) organized into two nested loops. In the outer loop, an adaptive artificial neural network-based proportional-integral-derivative (ANN-PID) controller is used for speed control. The ANN-PID is divided into two stages: the first stage includes an adaptive ANN speed estimator, and the second stage includes an adaptation algorithm that fine-tunes both the weights and biases of the ANN estimator and the parameters of the PID controller. In the internal loop, a predictive current controller is used to control IM currents using neural networks. Specifically, the neural predictive controller (NPC) approaches the control problem by presenting it as an optimization problem using a neural predictor for IM currents. The considered objective function includes two elements: the current tracking error and the electromagnetic torque ripple. This function is computed over a given time horizon informed by predictions of IM currents. The particle swarm optimization (PSO) algorithm is applied to determine the optimal solution for this optimization task. The effectiveness of the hybrid control scheme is demonstrated by simulation results obtained using Matlab/Simulink, highlighting its superiority over conventional control methods. The proposed hybrid control is characterized by a reduction in torque ripple and overshoot, while also showing robustness to variations in load, rotor resistance, and rotor inductance. Comparisons with an ANN controller and a fuzzy PI controller further demonstrate the superior performance of the hybrid controller in handling nonlinear dynamics and maintaining control accuracy under various operating scenarios.

Nonlinear Dynamics Analysis of Handgrip Strength Using the Poincaré Plot Method Through Video Processing Techniques

Background/Objectives: The aim of this study was to analyze the nonlinear dynamics of handgrip strength (HGS) in young adults, focusing on hand dominance, by employing the Poincaré plot method to assess short- and long-term variability utilizing dynamometry and video motion capture during sustained isometric contractions. Methods: A cross-sectional exploratory study was conducted on 30 healthy subjects (mean age 21.6 ± 1.3 years, 13 males and 17 females), measuring HGS for both the dominant hand (DH) and nondominant hand (NDH) using a Saehan hydraulic dynamometer during 25-s sustained isometric contractions. A GoPro HERO11 Black camera recorded the dynamometer’s needle movements, and the video data were analyzed using Kinovea software. Angular values were converted to force using a calibration-based formula, and the Poincaré plot computed variability indices (short-term variability—SD1, long-term variability—SD2, ratio SD1/SD2, and area of the fitting ellipse) for each hand in relation to HGS and angular velocity (AV). Data analysis included descriptive and inferential statistics. Results: We demonstrated a strong correlation between mechanical and video measurements (p ≤ 0.001), confirming the reliability of the video method. The findings highlight the importance of nonlinear analysis in understanding neuromuscular function and fatigue, revealing significant correlations among HGS, AV, Poincaré indices, and fatigue levels in both hands (p ≤ 0.001). Increased maximum HGS and AV correlated with higher nonlinear variability in force production. Conclusions: This study confirms the reliability of the proposed video-based HGS assessment and demonstrates the effectiveness of Poincaré plot analysis for capturing nonlinear variability in HGS.

Digital economy, technology, and urban carbon emissions nexus: an investigation using the threshold effects and mediation effects tests

IntroductionThis study aims to explore the mechanisms by which the digital economy influences urban carbon emissions in China, with a particular focus on potential threshold effects and the mediating role of technology. As the digital economy grows, it impacts various environmental metrics, including carbon emissions, necessitating a deeper understanding of its nonlinear dynamics and implications for sustainable urban development.MethodsUsing panel data from 286 prefecture-level cities in China spanning from 2012 to 2021, we apply threshold effect models and mediation effect tests. The threshold effect model is employed to investigate non-linear characteristics of the digital economy’s impact on carbon emissions, while the mediation effect model assesses the role of technology as an intermediary in this relationship.ResultsThe threshold effect model reveals a single threshold in the impact of the digital economy on urban carbon emissions, indicating a nonlinear relationship. Initially, the influence of the digital economy on emissions is weak, but as the digital economy develops, its effect becomes more pronounced. The mediation effect model demonstrates that technological advancement can offset the increase in emissions associated with digital economic growth, thus showcasing technology’s potential to mitigate environmental impacts.DiscussionThe findings suggest that while the digital economy generally promotes urban carbon emissions, its impact is non-linear and mitigatable through technological innovation. To curb emissions in urban areas, fostering technological innovation and supporting green technology research and development are critical. Moreover, enhancing management and supervision within the digital economy sector can contribute to balancing economic growth with environmental goals. These insights are valuable for policymakers striving to harmonize digital economic expansion with sustainable environmental practices.

Stationary scalar clouds around Kerr-Newman black holes

Abstract This study investigates scalar clouds around Kerr-Newman black holes within the Einstein-Maxwell-scalar model. Tachyonic instabilities are identified as the driving mechanism for scalar cloud formation. Employing the spectral method, we numerically compute wave functions and parameter space existence domains for both fundamental and excited scalar cloud modes. Our analysis demonstrates that black hole spin imposes an upper limit on the existence of scalar clouds, with excited modes requiring stronger tachyonic instabilities for their formation. These findings lay the groundwork for exploring the nonlinear dynamics and astrophysical implications of scalar clouds.

Intelligent multi-parameter control of a rectangular pulse in a passively mode-locked fiber laser

Rectangular pulses with tunable width and intensity in fiber lasers are critical for the study of nonlinear pulse dynamics and applications of nanosecond laser sources. However, due to the complex nonlinear dynamics within the laser cavity, precisely controlling multiple parameters of the rectangular pulses in fiber lasers remains challenging. Here, we propose an approach for intelligently controlling the intensity and width of rectangular pulse using an improved particle swarm optimization (PSO) algorithm in a passively mode-locked fiber laser with a nonlinear polarization rotation (NPR) technique. By automatically adjusting the electronic polarization controller (EPC) and pump power, multiple parameters of the output rectangular pulse can be effectively tailored, and thus, to desirable ones. This enables the flexible setting of the intensity and width of the rectangular pulse within the permissible range in a passively mode-locked fiber laser. Our approach provides a promising way to meet the diverse demands of seed laser source in scientific and engineering fields.

Model-Free Filter-Based Trajectory Tracking Controller for Two-Wheeled Vehicles Through Pole-Zero Cancellation Technique

Considering the nonlinear dynamics, this paper devises an advanced position trajectory tracking controller with a model-free filter for two-wheeled vehicle (TWV) applications. The proposed technique preserves a simple structure in the form of the proportional–integral (PI) controller involving the model-free filter and nonlinearly structured feedback gains, which make the following contributions: (a) the proposed filter smooths the position and yaw angle measurements according to the first-order convergence rate without any model information; and (b) the PI control with the nonlinearly structured feedback gains robustly stabilizes the position and yaw angle errors along the desired first-order system to accomplish the trajectory tracking mission, which is obtained by the pole-zero cancellation (PZC) in the presence of modeling errors. MATLAB/Simulink was used to emulate the resulting feedback system and validate the effectiveness of the proposed technique.

Nonlinear Stress-Induced Transformations in Collagen Fibrillar Organization, Disorder and Strain Mechanisms in the Bone-Cartilage Unit.

By developing a 3D X-ray modeling and spatially correlative imaging method for fibrous collagenous tissues, this study provides a comprehensive mapping of nanoscale deformation in the collagen fibril network across the intact bone-cartilage unit (BCU), whose healthy functioning is critical for joint function and preventing degeneration. Extracting the 3D fibril structure from 2D small-angle X-ray scattering before and during physiological compression reveals of dominant deformation modes, including crystallinity transitions, lateral fibril compression, and reorientation, which vary in a coupled, nonlinear, and correlated manner across the cartilage-bone interface. A distinct intermolecular arrangement of collagen molecules, and enhanced molecular-level disorder, is found in the cartilage (sliding) surface region. Just below, fibrils accommodate tissue strain by reorientation, which transitions molecular-level kinking or loss of crystallinity in the deep zone. Crystalline fibrils laterally shrink far more (20×) than they contract, possibly by water loss from between tropocollagen molecules. With the calcified plate acting as an anchor for surrounding tissue, a qualitative switch occurs in fibrillar deformation between the articular cartilage and calcified regions. These findings significantly advance this understanding of the complex, nonlinear ultrastructural dynamics at this critical interface, and opens avenues for developing targeted diagnostic and therapeutic strategies for musculoskeletal disorders.

Modeling and analysis of nonlinear dynamics of axisymmetric vector nozzle based on deep neural network

Abstract The axisymmetric nozzle mechanism is the core part for thrust vectoring of aero engine, which contains complex rigid-flexible coupled multibody system with joints clearance and significantly reduces the efficiency in modeling and calculation, therefore the kinematics and dynamics analysis of axisymmetric vectoring nozzle mechanism based on deep neural network is proposed. The deep neural network model of the axisymmetric vector nozzle is established according to the limited training data from the physical dynamic model and then used to predict the kinematics and dynamics response of the axisymmetric vector nozzle. This study analyses the effects of joint clearance on the kinematics and dynamics of the axisymmetric vector nozzle mechanism by a data-driven model. It is found that the angular acceleration of the expanding blade and the driving force are mostly affected by joint clearance followed by the angle, angular velocity and position of the expanding blade. Larger joint clearance results in more pronounced fluctuations of the dynamic response of the mechanism, which is due to the greater relative velocity and contact force between the bushing and the pin. Since axisymmetric vector nozzles are highly complex nonlinear systems, traditional numerical methods of dynamics are extremely time-consuming. Our work indicates that the data-driven approach greatly reduces the computational cost while maintaining accuracy, and can be used for rapid evaluation and iterative computation of complex multibody dynamics of engine nozzle mechanism.

Novel reinforcement learning technique based parameter estimation for proton exchange membrane fuel cell model

Proton Exchange Membrane Fuel Cells (PEMFCs) offer a clean and sustainable alternative to traditional engines. PEMFCs play a vital role in progressing hydrogen-based energy solutions. Accurate modeling of PEMFC performance is essential for enhancing their efficiency. This paper introduces a novel reinforcement learning (RL) approach for estimating PEMFC parameters, addressing the challenges of the complex and nonlinear dynamics of the PEMFCs. The proposed RL method minimizes the sum of squared errors between measured and simulated voltages and provides an adaptive and self-improving RL-based Estimation that learns continuously from system feedback. The RL-based approach demonstrates superior accuracy and performance compared with traditional metaheuristic techniques. It has been validated through theoretical and experimental comparisons and tested on commercial PEMFCs, including the Temasek 1 kW, the 6 kW Nedstack PS6, and the Horizon H-12 12 W. The dataset used in this study comes from experimental data. This research contributes to the precise modeling of PEMFCs, improving their efficiency, and developing wider adoption of PEMFCs in sustainable energy solutions.

Hot carrier transfer from plasmon decay in Ag20at H-Si(111) surface: real-time TDDFT simulation in Wannier gauge.

Plasmon decay is believed to play an essential role in inducing hot carrier transfer at the interfaces between plasmonic nanoparticles and semiconductor surfaces. In this work, we employ real-time time-dependent density functional theory (RT-TDDFT) simulation in the Wannier gauge to gain quantum-mechanical insights into the nonlinear dynamics of the plasmon decay in the Ag20nanoparticle at a semiconductor surface. The first-principles simulations show that the plasmon decay is more than two times faster when the Ag20nanoparticle is adsorbed on a hydrogen-terminated Si(111) surface, taking place within 100 femtoseconds of the plasmon excitation. Hot carrier transfer across the interface is observed as the plasmon decay takes place, and nearly 30% of holes are generated deep in the valence band of the semiconductor surface. The use of Wannier gauge in RT-TDDFT simulation is particularly convenient for gaining quantum-mechanical insights into non-equilibrium electron dynamics in complex heterogeneous systems.

COMPARATIVE ANALYSIS OF RF, SVR WITH GAUSSIAN KERNEL AND LSTM FOR PREDICTING LOAN DEFAULTS

This investigation elucidates the paramount endeavour of predicting loan defaults, which is imperative for the efficacious management of financial risk and the overall stability of financial institutions. Conventional statistical methodologies frequently encounter challenges in effectively capturing the nonlinear and sequential dynamics inherent in financial data, thereby necessitating the examination of more sophisticated machine learning methodologies. This research reports an experimental-based comparative evaluation of three ML and DL models—Long Short-Term Memory (LSTM) networks, Random Forest (RF), and Support Vector Regression (SVR)—to assess their efficacy in forecasting loan defaults. The models are evaluated using metrics such as Mean Squared Error (MSE), F1 score, and Accuracy, and their proficiency in addressing imbalanced datasets and elucidating intricate data relationships is highlighted. The results indicate that while the Random Forest model surpasses its counterparts in terms of accuracy and MSE, the LSTM model exhibits considerable potential in managing imbalanced data, as evidenced by its stable F1 score. Although SVR reveals competitive precision, it exhibits deficiencies in addressing class imbalance. The ANOVA analyses substantiate that the disparities in model performance are statistically significant. The research acknowledges that both the LSTM and SVR models remain in the developmental stages, with ongoing initiatives aimed at refining these models through hyperparameter optimization and advanced architectural frameworks to enhance their predictive efficacy in practical applications.

The critical impact of remote pilot modelling in evaluation of detect-and-avoid systems explained for ACAS Xu

Detect-and-avoid (DAA) systems for remotely piloted aircraft systems (RPAS) can provide remain well clear (RWC) guidance as well as shorter term resolution advisories (RAs) for collision avoidance, which are both provided in the vertical and horizontal planes. Simulation-based studies for large sets of encounter scenarios are used in the development and evaluation of DAA systems, which encompass safety and operational acceptability of the DAA supported operations. Given the key role of the remote pilot (RP) in responding to RWC guidance and RAs, a RP model is an essential element in such simulations. This paper describes the development of a RP model for evaluation of encounter scenarios involving the ACAS Xu DAA system. The model describes RP situation awareness (perception, comprehension, projection) as basis for decision-making, modes for responding to RAs and/or RWC guidance, response delays, response strengths, and the flight control actions. The RP model includes deterministic and stochastic settings. It is integrated in a simulation environment for encounters of manned and/or unmanned aircraft, the involved DAA and airborne collision avoidance systems, the surveillance and communication systems, and the human operators. Simulation results are provided for a set of encounters between pairs of RPAS both having ACAS Xu for various configurations of the RP model, and for cases with and without sensor errors. The results show that there can be large differences between the results of deterministic and Monte Carlo simulations, indicating that limited sensor errors can have a large impact on the nonlinear system dynamics. Furthermore it is shown that deadlock conditions can exist where the RPAS show oscillatory behaviour and do not manage to effectively pass each other, dependent on the encounter geometry and RP model settings. It is advised to perform a broad sensitively study for RP performance and to study extending the scope of DAA systems to include guidance for efficiently returning to mission without triggering new conflicts.