Behavior Of Nonlinear Systems Research Articles

Multicomponent nonlinear fractional Schrödinger equation: On the study of optical wave propagation in the fiber optics

In this article, we investigate the soliton wave dynamics of the fractional three-component coupled nonlinear Schrödinger equation. This equation is considered as a fundamental tool for describing the behavior of optical pulses in optical fibers. There is increasing interest in studying these equations as they can be used to explain a wide range of complex physical phenomena in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. In order to obtain the required solutions, the first step is to apply the complex wave transformations with β-fractional derivative to obtain the nonlinear ordinary differential equations of the governing model. Furthermore, by applying the novel integration methods known as generalized Arnous method and multivariate generalized exponential rational integral function approach, different type of soliton solutions are extracted. Different sets and values of the physical parameters are used to study the optical soliton solutions of the studied system. Based on a comparative analysis of our results with existing techniques, this study concludes that our proposed solutions are novel. The results described in this work are able to enhance the nonlinear dynamical behavior of a given system and confirm the effectiveness of the methods used. Furthermore, the different graphs are sketched to visualize the solutions behavior with various parametric values. It is anticipated that obtained solutions will be significant in the study of wave propagation and other related fields.

Extraction of nonlinearity in neural networks with Koopman operator

Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode decomposition, and the tensor-train format. The Koopman operator approach has been recently developed in physics and nonlinear sciences; the Koopman operator deals with the time evolution in the observable space instead of the state space. Since we can replace the nonlinearity in the state space with the linearity in the observable space, it is a hopeful candidate for understanding complex behavior in nonlinear systems. Here, we analyze learned neural networks for the classification problems. As a result, the replacement of the nonlinear middle layers with the Koopman matrix yields enough accuracy in numerical experiments. In addition, we confirm that the pruning of the Koopman matrix gives sufficient accuracy even at high compression ratios. These results indicate the possibility of extracting some features in the neural networks with the Koopman operator approach.

Identification of climatic tipping points and transitions in Chinese loess grain-size records utilizing nonlinear time series analysis

As one of the most important terrestrial sediments, Chinese loess provides valuable information on regional and global climatic and environmental changes and holds great potential for studying on nonlinear behaviors of the East Asian monsoon system. Utilizing objective and quantitative methods to identify tipping points and climate transitions in paleoclimatic records can help us understand the climatic change in the Chinese Loess Plateau (CLP). This study explores critical tipping points and nonlinear climate transitions within the CLP using the Chiloparts record, a comprehensive 2600-ka paleoclimate dataset. We pinpointed potential tipping points using recurrence quantification analysis and the augmented Kolmogorov-Smirnov test, ultimately leading to 15 critical tipping points. We argued that these 15 tipping points represent some of the most significant climatic changes recorded in the Chinese loess paleoclimate record. Employing recurrence quantification analysis, recurrence networks, and visibility graphs, we also identified several climate transitions and provided some nonlinear information, including the Mid-Pleistocene Transition (MPT) as well as the Mid-Brunhes Transition (MBT). We particularly highlight a significant climatic regime transition around 500 ka that may reflect a nonlinear response to variations in the Atlantic Meridional Overturning Circulation (AMOC). Our research also contributes to the understanding of the complex interplay between loess deposition, environmental change, and tectonic activity, emphasizing the need for further investigations to elucidate the mechanisms driving these transitions.

Bifurcation Analysis and Chaos Control of Carrier Phase-Shifted Cascaded H-Bridge Inverter

Cascaded H-bridge inverters, which belong to strongly nonlinear time-varying system with complex dynamics, have been widely used in high-voltage and high-power engineering fields. In this paper, a carrier phase-shifted sinusoidal pulse-width modulation cascaded H-bridge inverter is taken as an example with piecewise analysis to establish the discrete iterative mathematical model. Furthermore, the nonlinear dynamic behavior of this inverter system is investigated using folding diagrams, spectrum diagrams, bifurcation diagrams, Lyapunov exponents, etc. We find that this inverter can exhibit multiperiod bifurcation, tangential bifurcation and paroxysmal chaos within certain ranges of control coefficients and other circuit parameters, which will influence the system’s stability seriously. On the basis of this discovery, the sinusoidal time-delay feedback control method is proposed. The difference between the load current of the controlled object and its own delay is used to form a feedback term, which is then fed into the sine function and proportional link to obtain the control term. Moreover, the Jacobian matrix of this feedback inverter system is derived, and the constraints on the feedback control coefficient are obtained based on the Jury criterion. Simulation results have verified the effectiveness of such a sinusoidal time-delay feedback control method, which can improve the stability and anti-interference of the system. The research can be used to provide some reference and guidance for the circuit design, debugging and control of cascaded H-bridge inverters.

Innovative coupling of s-stage one-step and spectral methods for non-smooth solutions of nonlinear problems

The behavior of nonlinear dynamical systems arising in mathematical physics through numerical tools is a challenging task for researchers. In this context, an efficient semi-spectral method is proposed and applied to observe the robust solutions for the mathematical physics problems. Firstly, the space variable is approximated by the Vieta-Lucas polynomials and then the s-stage one-step method is applied to discretize the temporal variable which transfers the problem in the form Cn+1=Cn+Δtϕ(x,t,Cn,F(un)). Novel operational matrices of integer order are developed to replace the spatial derivative terms presented in the discussed problem. Related theorems are included in the study to validate the approach mathematically. The proposed semi-spectral schemes convert the considered nonlinear problem to a system of linear algebraic equations which is easier to tackle. We also accomplish an investigation on the error bound and convergence to confirm the mathematical formulation of the computational algorithm. To show the accuracy and effectiveness of the suggested computational method numerous test problems, such as the advection-diffusion problem, generalized Burger-Huxley, sine-Gordon, and modified KdV–Burgers’ equations are considered. An inclusive comparative examination demonstrates the currently suggested computational method in terms of credibility, accuracy, and reliability. Moreover, the coupling of the spectral method with the fourth-order Runge-Kutta method seems outstanding to handle the nonlinear problem to examine the precise smooth and non-smooth solutions of physical problems. The computational order of convergence (COC) is computed numerically through numerous simulations of the proposed schemes. It is found that the proposed schemes are in exponential order of convergence in the spatial direction and the COC in the temporal direction validates the studies in the literature.

A novel robust MPC scheme established on LMI formulation for surge instability of uncertain compressor system with actuator constraint and piping acoustic

This paper presents a new control method for surge instability of the compressor system. Due to the importance of the active control approach in improving the efficiency of the compressor system, a new scheme based on the model predictive control (MPC) technique has been considered to control surge which gives the benefits of control signal optimization by considering the constraints on states and input. Because of designing a novel MPC by using of linear matrix inequality scheme, the optimization problem is solved in less time and with less complexity. The proposed method is able to consider the limitation of the close coupled valve actuator and also covers the uncertainty on the model. In addition, the developed model describes the nonlinear behaviour of the compressor system and handles the effects of the pipe on surge instability. Using Lyapunov theory, the stability of the closed-loop system under the proposed robust active controller is shown. The simulation results show the high pressure and high efficiency operation of the system under study in different operating conditions.

On a nonlinear behavior of an aeroelastic system with quartic stiffness

On a nonlinear behavior of an aeroelastic system with quartic stiffness

Decomposition solutions and Bäcklund transformations of the B-type and C-type Kadomtsev–Petviashvili equations

This paper introduces a modified formal variable separation approach, showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev–Petviashvili (BKP) equation. Through the application of this approach, we successfully ascertain decomposition solutions, Bäcklund transformations, the Lax pair, and the linear superposition solution associated with the aforementioned equation. Furthermore, we expand the utilization of this technique to the C-type Kadomtsev–Petviashvili (CKP) equation, leading to the derivation of decomposition solutions, Bäcklund transformations, and the Lax pair specific to this equation. The results obtained not only underscore the efficacy of the proposed approach, but also highlight its potential in offering a profound comprehension of integrable behaviors in nonlinear systems. Moreover, this approach demonstrates an efficient framework for establishing interrelations between diverse systems.

The masking technique for forced nonlinear oscillator stability behavior analysis using the non-perturbative approach

The study utilized the masking technique to explore the stability behavior of a forced nonlinear oscillator through the non-perturbative approach, with a particular focus on a Van der Pol oscillator subjected to external force, characterized by both cubic and quadratic nonlinearities. The application of the non-perturbative method (NPM) in conjunction with the masking technique was a pivotal aspect of this research, transforming the inherently non-homogeneous, nonlinear system into a homogeneous linear system. This transformation was crucial as it simplified the complex dynamics of the system, rendering it more amenable to analysis. Through this method, the research successfully established the system’s overall frequency, meticulously accounting for the impact of the periodic external force. The study also identified a distinct type of resonance response, where the system’s frequency incorporates the excited frequency in a nonlinear relationship. The masking technique proved to be an invaluable tool for examining the stability behavior of forced vibrations in oscillators via the NPM, providing profound insights into stability under external forces and enhancing the understanding and control of oscillatory behaviors in nonlinear dynamical systems. A critical confirmation of the current methodology is provided by the remarkable agreement found between the numerical solution and the provided analytical solution. This agreement shows that the analytical method produces trustworthy predictions and appropriately describes the system’s behavior. The plotted stability diagrams, which demonstrate that the model’s simulation of stability behavior is consistent with observed events, particularly resonance phenomena, offer further validity for the findings. In the resonance case, the effects of the damping coefficient and the external force’s magnitude are significant. The results of the analysis show that an increase in the damping coefficient has a destabilizing effect that causes unstable zones to expand. In contrast, in the resonance state, the quadratic and cubic nonlinearity factors both contribute to stabilization. Understanding how various system factors impact stability dynamics particularly in relation to resonance phenomena is made easier with the help of this insight.

Neural network survivability approach of a wave energy converter considering uncertainties in the prediction of future knowledge

To tune the wave energy converter (WEC) controller parameters such as damping to reduce the line force during extreme wave conditions, future knowledge of the line force is required. To achieve this, the incoming wave and system state should be predicted for a few seconds in the future. It is rather an arduous task to predict the future knowledge of waves and the system’s dynamic when dealing with breaking and steep waves, and the system is subject to various nonlinear forces. The classical model-based control strategies often rely on linear assumptions to estimate the WEC dynamics for the sake of simplicity. Unlike the model-based, the data-driven approaches are free from modeling errors and the algorithms are trained over the true and noisy data to predict non-linear system behaviors. Using data-driven approaches, we are able to model nonlinear dynamics. However, new questions emerge on the accuracy of the future wave and system state predictions, and how this uncertainty propagates into the final prediction of the line force. As incorrect damping may lead to excessive line force and detrimental damage to the system, these are the knowledge gaps that need to be addressed. The main purpose of this paper is to answer these questions through a survivability strategy for wave energy converters by providing a realistic perspective on the implementation of the neural network approaches by accounting for the errors in the input data. For this purpose, a series of neural networks is designed that first predicts the surface elevation for 0.36 s ahead, i.e. corresponding to 2 s in the full-scale WEC. This future knowledge of the wave elevation is then used to predict the system state (i.e. power take-off (PTO) translator position) for the same prediction horizon based on the PTO damping. This information is then fed to a convolutional neural network (CNN) that predicts the peak line force 0.36 s ahead. This paper also evaluates the predictive capabilities of neural network (NN) models, comparing them to classical autoregressive (AR) and Kalman filter methods. While the AR model exhibits slightly higher accuracy in fixed PTO system configurations, it falters in providing real-time predictions when system parameters undergo variations. In contrast, the NN prediction model excels by establishing a robust relationship between system configuration and output signals. Especially noteworthy is its ability to outperform classical methods with minimal training on a selective set of system configurations. Then, the sensitivity of the peak line force prediction to the uncertainties in the input data from NN models and the prediction horizon is analyzed. The neural network models are trained over the experimental data subjected to extreme sea states for a point absorber wave energy converter. The results suggest that the accuracy of the surface elevation prediction has an insignificant direct effect on the peak force prediction model. However, these uncertainties are reflected in the PTO translator position prediction, and the model is considerably sensitive to the accuracy of this prediction. This sensitivity nonetheless is less notable for higher PTO damping values.

Performance analysis of various numerical methods for predicting monopile response under machine induced vibration

In this study, we verify the accuracy of the results obtained using two different numerical methods to simulate a pile-supported machine foundation under vertical vibration. To achieve this, finite element and finite difference methods, available as PLAXIS 3D and FLAC 3D, respectively, are selected for the study. A model consisting of a monopile with a diameter of 0.166 m and a length of 5.8 m is modelled to support the vibratory load induced by the rotary machine. A linear elastic model is used for the pile material and Mohr-Coulomb failure criterion is used for the soil. An analysis is performed to determine the frequency-versus-amplitude response of the monopile subjected to rotary-machine-induced vertical vibrations with different dynamic load intensities (0.735, 1.448, 2.117, and 2.721 Nm). The results obtained from both numerical analyses are compared with the experimental results available in the literature. Both numerical methods effectively simulate the nonlinear behavior of the soil-pile system, as observed in the experimental results. Based on the results, it is deduced that the finite element method simulated more harmonious results than the finite difference method compared with the experimental results, with more computational efficiency.

Bayesian Back Analysis of Axially Loaded Pile Response Using Fibre Optic Strain Data

The load-transfer method has been extensively used to evaluate the deformation behavior of foundation piles, with the nonlinear load-settlement behavior of a pile-soil system modeled using load-transfer curves. Although load-transfer models have a considerable impact on the pile response, the model parameters are usually estimated empirically from soil parameters using transformation models, and the associated uncertainties are often neglected. Fiber optic sensing technology provides detailed axial strain information along the entire length of a pile; however, the full potential of such utilization has not yet been realized. This paper presents a Bayesian back analysis method for statistical descriptions of load-transfer curves and pile responses based on fiber optic measurement. A pile test case study is used to illustrate the proposed method, and several candidate model configurations are compared. The results show that the predicted pile response generally matches the measured data, and the quantified uncertainty allows for a better understanding of the possible ranges of the pile response, in addition to the single best-estimate result.

High-performance steering tracking control of open circuit variable-speed pump-controlled steering system for heavy-duty vehicles based on flow nonlinearity compensation

Heavy-duty vehicles with long bodies, a large number of axles and large loads are subject to increasingly high requirements for precise steering technology due to the increasing trend toward energy conservation and intelligent assisted driving as well as variable driving conditions. In this paper, an energy-efficient open circuit variable-speed pump-controlled steering system (OPCEHSSS) adapted for heavy loads is used, but its strong flow output nonlinearity and system nonlinear dynamic behavior greatly impede the steering performance. Therefore, in order to reduce the influence of the flow leakage of the fixed-displacement pump on the system and to ensure that the flow output of the system matches the control model, a mapping model based on the fitting of a two-layer neural network algorithm with a dynamic real-time compensation strategy (FNC) is proposed. In addition, considering the strong robustness of the system even under parameter uncertainty and unknown disturbance, a complex nonlinear mathematical model is established based on OPCEHSSS physical characteristics, and a dual-objective control strategy of steering angle and pressure based on sliding mode control (SMC) is proposed. However, in order to reduce the influence of high-order switching discontinuity on the steering and ensure the fast convergence of the control system, a fast super twisting algorithm (STA) based on double saturation function of the boundary layer is proposed. The experimental results show that the three different controllers can effectively reduce the steering angle error after the introduction of FNC. And in the case of a single axle loaded with 6 tons, the improved new FNC+STA integrated dual-objective control strategy improves the accuracy by 53.16% compared with PID and 40.67% compared with SMC. The steady-state error is maintained within 0.9°, realizing the high-performance steering tracking control of OPCEHSSS for heavy vehicles.

Transient breathing dynamics of dissipative soliton in an ultrafast laser

The occurrence of periodically oscillatory behaviors in various nonlinear dissipative systems is known as breathing dynamics, which holds potential applications in spectroscopy. Herein, we have employed both experimental and numerical methods to investigate the breathing dynamics of dissipative soliton induced by Q-switched modulation in a mode-locked fiber laser. The findings indicate that the dynamics of breathing significantly influences the buildup stage of both stationary and breathing dissipative solitons. The breathing rate, breathing duration and breathing period are quite sensitive to the pump power. Numerical simulations are employed to generate similar breathing dynamics within the context of a model that combines equations describing the population inversion in a mode-locked laser. These obtained results provide confirmation that the Q-switching modulation is responsible for the initiation of breathing oscillations, and present novel prospects for the development of different operational frameworks for ultrafast lasers.

On the optical wave structures to the fractional nonlinear integrable coupled Kuralay equation

This paper is mainly concerning the study of truncated M-fractional Kuralay equations that have applications in numerous fields, including nonlinear optics, ferromagnetic materials, signal processing, engineering fields and optical fibers. Due to its ability to clarify a wide range of sophisticated physical phenomena and reveal more dynamic structures of localized wave solutions, the Kuralay equation has captured a lot of attention in the research field. The newly designed integration methods, known as the modified Sardar subequation method and enhanced modified extended tanh expansion method are used as solving tools to validate the solutions. The goal of this study is to extract several kinds of optical solitons, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. Due to the many potential applications for superfast signal routing techniques and shorter light pulses in communications, the optical propagation of soliton in optical fibers is now a topic of significant interest. 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. In addition, exponential, periodic, hyperbolic solutions are generated. The applied approaches are efficient in explaining fractional nonlinear partial differential equations by providing pre-existing solutions and also producing new solutions by combining results from multiple processes. Additionally, we plot the contour, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The results of this study show the effectiveness of the approaches adopted and help enhance comprehension of the nonlinear dynamical behavior of specific systems. We expect that a substantial amount of engineering model specialists will greatly benefit from our work. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

Efficient and accurate flexible multibody dynamics modeling for complex spacecraft with integrated control applications

This study presents a novel flexible multibody dynamics modeling method tailored to spacecraft with intricate motion features such as multi-axis antenna actuation, robotic manipulations, and space station module rotation. Using a floating base and a tree-topology structure, the model effectively simulates the kinematics and dynamics of large-angle joint rotations and elastic deformations, leveraging the Lagrangian framework and finite element analysis. An advanced augmented proportional–derivative (APD) control scheme is also introduced, incorporating system dynamics for enhanced predictive control, accommodating complex interactions and nonlinear system behaviors. Our modeling approach, compared with the commercial Adams software, shows similar system responses while reducing computation time by about 70%, highlighting its efficiency and accuracy. Moreover, incorporating the APD strategy into our system enhances tracking precision, achieving a 90% reduction in error compared with conventional proportional–derivative controls, underscoring the benefits of combining dynamic modeling with control improvements.

Hybrid of Meta-Heuristic Techniques Based on Cuckoo Search and Particle Swarm Optimizations for Solar PV Systems Subjected to Partially Shaded Conditions

Solar energy has a significant role in meeting rising energy demand while reducing environmental impact. Solar radiation and temperature are important factors on which PV energy production depends, but its optimal operation point is influenced by variations in the aforementioned environmental factors. The nonlinear behavior of the solar system and the variable nature of environmental conditions make determining the optimal operation point difficult. To overcome these difficulties, maximum power point tracking (MPPT) finding techniques are used to extract the optimal power from the photovoltaic energy system. The behavior of MPPT varies for different weather conditions, such as partial shading conditions (PSC), and uniform irradiance conditions. Conventional techniques are simple, quick, and efficient for tracing the MPP quickly, but they are limited to uniform weather conditions. In addition, these techniques don't achieve the Global Maxima (GM) and mostly stay stuck at the Local Maxima (LM). The Meta-Heuristic techniques aid in finding the GM, but their primary disadvantage is that they take a longer time to trace the Global Maxima. This study addresses the problem by combining Cuckoo Search (CS) and Particle Swarm Optimization (PSO) algorithms, leading to a hybrid (CSPSO) technique to extract the global maximum (GM). To verify the effectiveness of the suggested technique, its performance is examined under three different irradiance patterns for different PV array configurations (such as 3S and 4S3P) through MATLAB simulation. The outcomes of CSPSO are compared with the prior well-known Meta-Heuristic techniques such as Cuckoo Search (CS), Particle Swarm Optimization (PSO), and Crow Search Algorithm (CSA). The results show the suggested technique excels over other techniques in terms of accuracy, tracking efficiency, and tracking speed. The suggested technique is capable of tracking GMPP with an average efficiency of 99.925% and an average tracking time of 0.13 s in all shading patterns studied.

Review on PID, fuzzy and hybrid fuzzy PID controllers for controlling non-linear dynamic behaviour of chemical plants

The chemical production process is tedious due to the integration of different types of equipment and variables. Designing the controller is crucial in the chemical industry due to the interactive and non-linear system behaviour. An intelligent autonomous controller can improve the operating efficiency of the industry. Although several controllers have been developed, different system failures are frequently reported. Hence, controllers such as proportional integral derivative (PID), fuzzy logic controller (FLC), and hybrid fuzzy PID (F-PID) applied in the chemical industries are critically reviewed in the paper. Initially, the PID controller-based approaches are reviewed for different purposes in the chemical industry. After that, the FLC-based controllers-based papers are reviewed. In order to satisfy the issues in both controllers, the H-PID controllers have been reviewed. This review paper will provide an effective solution for operation control in the chemical industry under different operating conditions.

Model-based Decision Support System Using a System Dynamics Approach to Increase Corn Productivity

Background: As the population increases, the need for corn products also increases. Corn is needed for various purposes, such as food consumption, industry, and animal feed. Therefore, increasing corn production is crucial to support food availability and the food industry. Objective: The objective of this project is to create a model to increase corn farming productivity using scenarios from drip irrigation systems and farmer field school programs. Methods: A system dynamics approach is utilized to model the complexity and nonlinear behaviour of the corn farming system. In addition, several scenarios are formulated to achieve the objective of increasing corn productivity. Results: Simulation results showed that adopting a drip irrigation system and operating a farmer field school program would increase corn productivity. Conclusion: The corn farming system model was successfully developed in this research. The scenario of implementing a drip irrigation system and the farmer field school program allowed farmers to increase corn productivity. Through the scenario of implementing a drip irrigation system, farmers can save water use, thereby reducing the impact of drought. Meanwhile, the scenario of the farmer field school program enables farmers to manage agriculture effectively. This study suggests that further research could consider the byproducts of corn production to increase the profits of corn farmers. Keywords: Corn Farming, Decision Support System, Modeling, Simulation, System Dynamics

Empirical dynamic modelling and enhanced causal analysis of short-length Culex abundance timeseries with vector correlation metrics

Employing Empirical Dynamic Modelling we investigate whether model free methods could be applied in the study of Culex mosquitoes in Northern Greece. Applying Simplex Projection and S-Map algorithms on yearly timeseries of maximum abundances from 2011 to 2020 we successfully predict the decreasing trend in the maximum number of mosquitoes which was observed in the rural area of Thessaloniki during 2021. Leveraging the use of vector correlation metrics we were able to deduce the main environmental factors driving mosquito abundance such as temperature, rain and wind during 2012 and study the causal interaction between neighbouring populations in the industrial area of Thessaloniki between 2019 and 2020. In all three cases a chaotic and non-linear behaviour of the underlying system was observed. Given the health risk associated with the presence of mosquitoes as vectors of viral diseases these results hint to the usefulness of EDM methods in entomological studies as guides for the construction of more accurate and realistic mechanistic models which are indispensable to public health authorities for the design of targeted control strategies and health prevention measures.