Behavior Of Dynamical Systems Research Articles

Modeling and Analysis of Actuators in Multi-Pump Waterjet Propulsion Systems

Waterjet propulsion, which generates thrust by ejecting water jets, has attracted significant attention in modern high-performance vessels due to its efficiency, superior cavitation resistance, and excellent maneuverability. While previous research has primarily concentrated on optimizing the overall performance of waterjet propulsion systems, insufficient attention has been paid to the detailed dynamic modeling of actuators in multi-pump systems, a critical component for improving system control precision. This paper addresses this gap by developing dynamic models for the reversing bucket and rudder angle actuators in marine waterjet propulsion systems. Based on an in-depth analysis of their working principles and operational parameters, transfer function models are established to simulate actuator performance under various conditions, including wear, hydraulic oil leakage, and external disturbances. Key influencing factors for each condition are identified, and corresponding parameter-setting models are constructed. The models’ response speed and steady-state accuracy are validated through step and ramp tests, confirming their effectiveness and reliability. The proposed model is verified with real measurement experiments and comparisons. The findings of this study contribute new insights into the dynamic behavior of multi-pump waterjet propulsion systems and provide a solid theoretical foundation for the future development of optimized control strategies in complex marine propulsion environments.

Dynamic behavior of multi-dimensional chaotic systems based on state variables and unknown parameters with applications in image encryption

Abstract To explore the impact of unknown terms and parameters on chaotic characteristics in chaotic systems, this paper examines the effects of state variables and unknown parameters. The study focuses on different combinations of linear, nonlinear, and constant terms It primarily investigates the role of multi-order state variables and their application to chaotic system models of varying dimensions. Firstly, by simulating a three-dimensional chaotic system, the paper analyzes how different combinations of nonlinear terms and initial conditions affect the system's chaotic behavior. Secondly, it evaluates the chaotic characteristics of a four-dimensional system, combining nonlinear terms with unknown parameters, using tools such as Lyapunov index diagrams, sample entropy, and dynamic trajectory plots. Finally, the paper integrates the constructed chaotic system with chaotic mapping to develop a two-level key chaotic image encryption system, thoroughly assessing its security and resistance to interference.

Advanced Adiabatic Compressed Air Energy Storage Systems dynamic modelling: Impact of the heat storage device

Advanced Adiabatic Compressed Air Energy Storage (AACAES) is a technology for storing energy in thermomechanical form. This technology involves several equipment such as compressors, turbines, heat storage capacities, air coolers, caverns, etc. During charging or discharging, the heat storage and especially the cavern will induce transient behavior of operating points, notably temperature, pressure, and volume flow. In contrast, the optimal use of turbomachinery requires it to be as stationary as possible. AACAES technology therefore requires transient modelling to optimize its design. This paper presents a modular and adaptable numerical tool capable of simulating the dynamic behavior of different thermomechanical storage systems. This tool is then applied to an AACAES system to analyze the impact of various configurations on the variability of volume flow. The aim is to optimize Round Trip Efficiency (RTE) while limiting the maximum variation in volume flow. First, the effect of the size of fixed-bed Thermal Energy Storage (TES) is analyzed. Then, we analyze the behavior of the system with heat management based on a heat exchanger and a heat transfer fluid. In addition, the effect of adding pressure control at the cavern inlet/outlet on the two previous variants is studied.

The applicability limits of the lowest-order substitute model for a cantilever beam system hard-impacting a moving base.

This paper examines the circumstances under which a one-degree-of-freedom approximate system can be employed to predict the dynamics of a cantilever beam comprising an elastic element with a significant mass and a concentrated mass embedded at its end, impacting a moving rigid base. A reference model of the system was constructed using the finite element method, and an approximate lowest-order model was proposed that could be useful in engineering practice for rapidly ascertaining the dynamics of the system, particularly for predicting both periodic and chaotic motions. The number of finite elements in the reference model was determined based on the calculated values of natural frequencies, which were found to correspond to the values of natural frequencies derived from the application of analytical formulas. The precision of the parameter identification and the outcomes yielded by the substitute model were validated through the calculation of the regions of stable periodic solutions using the analytical Peterka method. Subsequently, the qualitative and quantitative limits of the substitute model's applicability were determined. The quantitative limits were delineated through the utilization of Lyapunov exponents and characteristics associated with the energy dissipation due to impacts and the average number of impacts per excitation period. These characteristics provide a foundation for the introduction of global distance measures of the dynamic behavior of diverse systems within a specified range of the control parameter.

Bifurcation Analysis in Dynamical Systems Through Integration of Machine Learning and Dynamical Systems Theory

Abstract Characterizing the nonlinear behavior of dynamical systems near the stability boundary is a critical step toward understanding, designing, and controlling systems prone to stability concerns. Traditional methods for bifurcation analysis in both experimental systems and large-dimensional models are often hindered either by the absence of an accurate model or by the analytical complexity involved. This paper presents a novel approach that combines the theoretical frameworks of nonlinear reduced-order modeling and stability analysis with advanced machine learning techniques to perform bifurcation analysis in dynamical systems. By focusing on a low-dimensional nonlinear invariant manifold, this work proposes a data-driven methodology that simplifies the process of bifurcation analysis in dynamical systems. The core of our approach lies in utilizing carefully designed neural networks to identify nonlinear transformations that map observation space into reduced manifold coordinates in its normal form where bifurcation analysis can be performed. The unique integration of analytical and data-driven approaches in the proposed method enables the learning of these transformations and the performance of bifurcation analysis with a limited number of trajectories. Therefore, this approach improves bifurcation analysis in model-less experimental systems and cost-sensitive high-fidelity simulations. The effectiveness of this approach is demonstrated across several examples.

Improving the Solution Procedure of Incremental Harmonic Balance Method for Multi-Degree-of-Freedom Self-Excited Vibration Systems

When applying the Incremental Harmonic Balance (IHB) method to solve the limit cycle in a self-excited system, the practice of fixing one of the harmonic coefficients effectively solves the problem that there are more unknowns than algebraic equations due to the presence of unknown angular frequencies in the periodic response. However, an inappropriate value for this fixed harmonic coefficient can significantly affect the convergence of subsequent Newton–Poisson iterations. To address this issue, we propose a technique that dynamically adjusts the value of the fixed harmonic coefficient, effectively improving the convergence and stability of the traditional IHB method and providing an efficient solution for the parametric study of self-excited systems. The efficiency and performance of our method in accurately predicting periodic solutions are demonstrated by its application to Van der Pol oscillators and predicting vortex-induced vibrations in cable-stayed structures. Numerical simulations show that the results obtained by the proposed method are very close to those obtained by the Runge–Kutta method. This study opens up a robust and efficient approach for analyzing and studying the dynamic behavior of complex self-excited systems.

Grand canonical Monte Carlo and deep learning assisted enhanced sampling to characterize the distribution of Mg2+ and influence of the Drude polarizable force field on the stability of folded states of the twister ribozyme.

Molecular dynamics simulations are crucial for understanding the structural and dynamical behavior of biomolecular systems, including the impact of their environment. However, there is a gap between the time scale of these simulations and that of real-world experiments. To address this problem, various enhanced simulation methods have been developed. In addition, there has been a significant advancement of the force fields used for simulations associated with the explicit treatment of electronic polarizability. In this study, we apply oscillating chemical potential grand canonical Monte Carlo and machine learning methods to determine reaction coordinates combined with metadynamics simulations to explore the role of Mg2+ distribution and electronic polarizability in the context of the classical Drude oscillator polarizable force field on the stability of the twister ribozyme. The introduction of electronic polarizability along with the details of the distribution of Mg2+ significantly stabilizes the simulations with respect to sampling the crystallographic conformation. The introduction of electronic polarizability leads to increased stability over that obtained with the additive CHARMM36 FF reported in a previous study, allowing for a distribution of a wider range of ions to stabilize twister. Specific interactions contributing to stabilization are identified, including both those observed in the crystal structures and additional experimentally unobserved interactions. Interactions of Mg2+ with the bases are indicated to make important contributions to stabilization. Notably, the presence of specific interactions between the Mg2+ ions and bases or the non-bridging phosphate oxygens (NBPOs) leads to enhanced dipole moments of all three moieties. Mg2+-NBPO interactions led to enhanced dipoles of the phosphates but, interestingly, not in all the participating ions. The present results further indicate the importance of electronic polarizability in stabilizing RNA in molecular simulations and the complicated nature of the relationship of Mg2+-RNA interactions with the polarization response of the bases and phosphates.

Digital Twin-Based Smart Feeding System Design for Machine Tools

With the continuous development of intelligent manufacturing technology, the application of intelligent feed systems in modern machine tools is becoming increasingly widespread. Digital twin technology achieves the monitoring and optimization of the entire life cycle of a physical system by constructing a virtual image of the system, while neural network controllers, with their powerful nonlinear fitting ability, can accurately capture and simulate the dynamic behavior of complex systems, providing strong support for the optimization control of intelligent feed systems. This article discusses the design and implementation of an intelligent feed system based on digital twins and neural network controllers. Firstly, this article establishes a mathematical model based on the traditional ball screw structure and analyzes the dynamic characteristics and operating mechanism of the system. Subsequently, the mathematical model is fitted using a neural network controller to improve control accuracy and system response speed. The experimental results demonstrate that the neural network controller shows good consistency in fitting traditional mathematical models, not only effectively capturing the nonlinear characteristics of the system but also maintaining stable control performance under complex operating conditions.

An adaptive reduction method for viscoelastic structures without approximation on viscoelasticity

Abstract Viscoelastic materials are often encountered in engineering applications, such as bonded assemblies, polymer structures, or structures with damping treatments. To simulate the dynamic behavior of large mechanical systems with viscoelastic materials, finite element (FE) models are commonly employed. However, the large size of these models can lead to significant computational costs, making model order reduction (MOR) often a necessary step for improving the computational efficiency. Recently, an adaptive Taylor-based second-order Arnoldi (AT-SOAR) algorithm was introduced, which addresses the frequency-dependency of viscoelastic materials. However, due to the Taylor-based approximation used in the viscoelastic behavior modelling, the resulting reduced order models (ROMs) may leave room for improvement, both from an accuracy as well as from an efficiency point of view. Hence, this work proposes a two-layer Krylov subspace (TLK) method that circumvents the viscoelastic model approximation. Additionally, a sequenced collection approach is used to augment the reduction basis from these two layers of Krylov subspaces. For automating ROM generation in line with specific error criteria, the TLK method is integrated with the adaptive algorithm in AT-SOAR (A-TLK). The proposed method is demonstrated through an adhesive single-lap model example, showing that A-TLK can generate smaller, more efficient ROMs compared to AT-SOAR under the same error tolerance.

An efficient coupled fluid flow-geomechanics model for capturing the dynamic behavior of fracture systems in tight porous media

This paper introduces an efficient hybrid numerical discretization method designed to address the coupled mechanical challenges of geomechanics and fluid flow during pressure depletion in tight reservoirs. Utilizing the extended finite element method, this approach solves the elastic deformation of rock, while the mixed boundary element method precisely calculates the unsteady fluid exchange between the matrix and fractures. These numerical schemes are integrated fully, with temporal dynamics managed through a fully implicit method that effectively characterizes fracture deformation and fluid flow in hydrocarbon development. Furthermore, this model incorporates embedded pre-treatment to represent hydraulic macro-fractures and considers the effects of proppant. It captures dynamic information regarding the matrix and minor natural fractures through the double-porosity effective stress principle and a dual-medium implicit fracture characterization method. Thus, the proposed hybrid model provides a comprehensive depiction of the complex interplay between the matrix, natural fractures, and hydraulic fractures. The model's accuracy is validated through various examples, highlighting its reliability. This research offers valuable theoretical insights for advancing the development of unconventional hydrocarbon resources.

Molecular Dynamic Simulation Study of Newly Cytotoxic 2-(Aminomethyl)Benzimidazole Derivatives as Tyrosine Kinase Inhibitors

Receptor tyrosine kinases (RTK) are considered one of the main targets in cancer therapy due to their high expression. Unfortunately, multiple molecular mechanisms of resistance have been identified, leading to drug resistance and toxicity, which increases the need to discover new structural tyrosine kinase inhibitors. Instead of the rigid molecular docking method, molecular dynamic simulations can treat both the ligand and the protein in a flexible way. This lets the receptor-binding site fit around the new ligand. Also, the effect of explicit water molecules can be studied directly, and very accurate binding free energies can be obtained. The cytotoxic study does not explain the mechanism by which the tested compound could act, so further costly biological studies are needed. So, molecular dynamics is used as a computational technique that simulates the dynamic behavior of molecular systems as a function of time. Using Maestro v 13.0.135 interface (Schrodinger, New York, NY, 2021), molecular dynamic simulation was done with two proteins (EGFR and HER2) that are co-crystallized with the same ligand of a dual EGFR/HER2 inhibitor (TAK-285), and then they were tested with compounds of highly cytotoxic activity (2g and 4g) of suspected dual TKI activity from a previous study. According to the resulted data that were shown in the simulation interactions diagram reports, we recognize that the 2g compound showed a good interaction complex with both 3POZ (EGFR) and 3RCD (HRE2) proteins, while only the 4 g-3RCD complex showed a good interaction report. So, 2g could be considered a dual EGFR/HER2 inhibitor and 4g as an HER2 inhibitor, and for further investigation, both compounds could be tested further with other biological studies, especially enzyme inhibitory assays with suspected promising results.

Random attractors for fractional stochastic reaction–diffusion systems with fractional Brownian motion

Fractional stochastic reaction–diffusion systems involving fractional Brownian motion (fBm) provide a comprehensive modeling framework for studying complex physical and biological phenomena. In this study, we investigate the dynamic behavior of solutions to fractional stochastic reaction–diffusion systems with fBm defined on Rn. Firstly, we establish the existence and uniqueness of solutions to the fractional stochastic reaction–diffusion systems with fBm. We also obtain uniform estimates for the solutions on average. Furthermore, we construct a mean random dynamical system based on the derived solutions. Finally, we prove the existence and uniqueness of weak pullback mean random attractors. The results of our investigation contribute to a deeper understanding of the complexities involved in reaction–diffusion processes, specifically considering the effect of fBm with long-range dependence and self-similarity properties. Additionally, our findings have broader applications, particularly in areas such as analyzing the dynamic behavior of complex systems and biological models.

Optimal Paradigms for Quantitative Modeling in Systems Biology Demonstrated for Spinal Motor Neuron Synthesis

Since the 1990s, Petri nets have been used in systems biology for quantitative modeling. Despite the increasing number of models developed during this period, doubts remain about their biological relevance. Although biological systems predominantly exhibit intracellular or cellular structures, the models rely largely on deterministic predictions, failing to capture the inherent randomness and uncertainties of such systems. The question arises whether these models accurately describe the dynamic behavior of biological systems. This paper introduces a methodology for selecting the appropriate modeling paradigms in systems biology. Initially, we construct a Petri net model and perform deterministic, stochastic, and fuzzy stochastic simulations. Then we perform various statistical tests to measure the discrepancies between the simulation results. Based on scale-density analysis, we determine the modeling approach that best approximates the biological system. Finally, we compare the results of the statistical tests and the scale-density analysis to identify the optimal modeling approach. We applied the proposed methodology to the synthesis of spinal motor neuron protein from the spinal motor neuron-2 gene. Analysis revealed significant discrepancies between the simulation results of different modeling paradigms. Due to the sparse nature of the underlying drug-disease network, we conclude that the fuzzy stochastic paradigm provides the most biologically relevant results. We predict drug combinations that could lead to an up to 149-fold increase in spinal motor neuron protein levels, indicating a promising treatment for the disease. This methodology has the potential for application to other gene-drug-disease networks and broader biological systems.

Generalized Gaussian Distribution Improved Permutation Entropy: A New Measure for Complex Time Series Analysis.

To enhance the performance of entropy algorithms in analyzing complex time series, generalized Gaussian distribution improved permutation entropy (GGDIPE) and its multiscale variant (MGGDIPE) are proposed in this paper. First, the generalized Gaussian distribution cumulative distribution function is employed for data normalization to enhance the algorithm's applicability across time series with diverse distributions. The algorithm further processes the normalized data using improved permutation entropy, which maintains both the absolute magnitude and temporal correlations of the signals, overcoming the equal value issue found in traditional permutation entropy (PE). Simulation results indicate that GGDIPE is less sensitive to parameter variations, exhibits strong noise resistance, accurately reveals the dynamic behavior of chaotic systems, and operates significantly faster than PE. Real-world data analysis shows that MGGDIPE provides markedly better separability for RR interval signals, EEG signals, bearing fault signals, and underwater acoustic signals compared to multiscale PE (MPE) and multiscale dispersion entropy (MDE). Notably, in underwater target recognition tasks, MGGDIPE achieves a classification accuracy of 97.5% across four types of acoustic signals, substantially surpassing the performance of MDE (70.5%) and MPE (62.5%). Thus, the proposed method demonstrates exceptional capability in processing complex time series.

Effects of periodic long-wave deviations on the dynamic behaviors of spur gear systems

Noise reduction plays a major role in the drive train of motor vehicles operating at higher speeds. Long-wave deviations of gear systems related to manufacturing and assembly errors, such as tooth pitch deviation and geometric eccentricity, exhibit circumferential variations and have been demonstrated to be significant contributors to noise generation. However, a comprehensive and effective model that considers multiple long-wave deviations simultaneously has seldom been studied. To fill this gap, a new numerical model of spur gear systems with long-wave deviations is established, in which the coupling effects of both tooth pitch deviation and geometric eccentricity are taken into consideration. A time-varying mesh stiffness (TVMS) analytical model for spur gear pairs is established, which considers the relationship of errors between pitch deviation and eccentricity. The time-varying contact state of the gear pair under periodic long-wave deviations is also analyzed. A translation-torsion coupled dynamic model is established to investigate the excitation behavior of gear pairs with periodic long-wave deviations. The accuracy of the TVMS and the dynamic model is verified through comparisons with reference and experimental results. Results show that gear pairs with long-wave deviations exhibit periodic fluctuations in TVMS compared to ideal gear pairs, accompanied by phase differences. The mesh stiffness impact phenomenon becomes less pronounced for higher gear precision under lower-load conditions. Conversely, the periodic vibration characteristics induced by eccentricity become less prominent for the lower gear precision level. The excitation behavior of the gear pair with pitch deviation is masked by eccentricity at lower rotational orders, but it still dominates at higher rotational orders. This method can predict the dynamic characteristics of gear transmission systems with periodic long-wave deviations, providing theoretical guidance for reducing the vibration and noise levels.

Modeling and control of dynamical biomechanical arm systems with elastic joints sensitive to the effect of an external load

In this study, a biomechanical model mimicking the human hand-arm system under heavy disk excitation is developed to define the stability threshold between the preload vibration and the stress of the human hand-arm system. The fully electromechanical system, consisting of a DC motor, a transmission system, and three discrete masses representing the upper arm, forearm, and hand lifting a heavy disk, is connected by shock absorbers and various springs. The challenge of mimicking the angular activity of the elbow joint in torsion and flexion was also included to assess its contribution to system stability and to study the absorption of mechanical energy in the human hand-arm system. Finally, the movements of the model were described by a differential matrix equation, and its analysis facilitates the understanding of the threshold of the chaotic behaviors observed in an oscillating arms system. Specifically, it explores how the motion of a DC motor can be regulated using a single controller parameter within the context of a multi-degree-of-freedom human hand-arm system. The study uses numerical integrations to analyze system behaviors, with an emphasis on the use of frequency spectra, Poincaré maps, and bifurcation diagrams for visualization and interpretation. The results indicate that the system exhibits chaotic behavior when subjected to certain conditions, particularly when the mass load exceeds 35 kg. Imposing motion on the mass block further intensifies the chaos, leading to manifestations such as strong oscillations and frequency-synchronization effects. These characteristics, exhibited by the idealized model, which imitates the human body through a mechanical model and computation of the motions of the body, play a vital role in various fields of ergonomics and sports biomechanics. Understanding the dynamic behaviors of such systems, especially in response to varying conditions, has significant implications for engineering applications.

Data-driven modeling of subharmonic forced response due to nonlinear resonance

Complex behavior in nonlinear dynamical systems often arises from resonances, which enable intricate energy transfer mechanisms among modes that otherwise would not interact. Theoretical, numerical and experimental methods are available to study such behavior when the resonance arises among modes of the linearized system. Much less understood are, however, resonances arising from nonlinear modal interactions, which cannot be detected from a classical linear analysis. Academic examples of such phenomena have been known, but no systematic method has been developed to detect and model nonlinear resonant interactions purely from numerical or experimental data. Here, we develop such a data-driven methodology that identifies nonlinear resonant response on low-dimensional spectral submanifolds (SSMs) of the dynamical system. Our approach is generally applicable to nonlinear resonances, but we specifically focus here on one particular behavior: subharmonic response in forced nonlinear systems without any resonance among the linearized frequencies of the unforced system. We first illustrate analytically how such a response is born out of a nonlinear resonance hidden in the conservative limit of the system. We then show how this effect can be identified and modeled purely from data. As our main example, we isolate and model previously unexplained response patterns in fluid sloshing experiments.

Dynamical mode recognition of coupled flame oscillators by supervised and unsupervised learning approaches

Combustion instability in gas turbines and rocket engines, as one of the most challenging problems in combustion research, arises from the complex interactions among flames influenced by chemical reactions, heat and mass transfer, and acoustics. Identifying and understanding combustion instability is essential for ensuring the safe and reliable operation of many combustion systems, where exploring and classifying the dynamical behaviors of complex flame systems is a core task. To facilitate fundamental studies, the present work concerned dynamical mode recognition of coupled flame oscillators made of flickering buoyant diffusion flames, which have gained increasing attention in recent years but are not sufficiently understood. The time series data of flame oscillators were generated through fully validated reacting flow simulations. Due to the limitations of expertise-based models, a data-driven approach was adopted. In this study, a nonlinear dimensional reduction model of variational autoencoder (VAE) was used to project the high dimensional data onto a 2-dimensional latent space. Based on phase trajectories in the latent space, both supervised and unsupervised classifiers were proposed for datasets with and without well-known labeling, respectively. For labeled datasets, we established the Wasserstein-distance-based classifier (WDC) for mode recognition; for unlabeled datasets, we developed a novel unsupervised classifier (GMM-DTW) combining dynamic time warping (DTW) and Gaussian mixture model (GMM). Through comparing with conventional approaches for dimensionality reduction and classification, the proposed supervised and unsupervised VAE-based approaches exhibit a prominent performance across seven assessment metrics for distinguishing dynamical modes, implying their potential extension to dynamical mode recognition in complex combustion problems.

A method for dynamic parameter identification of an industrial robot based on frequency response function

AbstractHaving accurate values of the dynamic parameters is necessary to characterize the dynamic behaviors of mechanical systems and for the prediction of their responses. To accurately describe the dynamic characteristics of industrial robots (IRs), a new method for dynamic parameter identification is proposed in this study with the goal of developing a real IR dynamics model that combines the multibody system transfer matrix method (MSTMM) and the nondominated sorting genetic algorithm‐II (NSGA‐II). First, the multibody dynamics model of an IR is developed using the MSTMM, by which its frequency response function (FRF) is calculated numerically. Then, the experimental modal analysis is conducted to measure the IR's actual FRF. Finally, the objective function of the minimum errors between the calculated and measured eigenfrequencies and FRFs are constructed to identify the dynamic parameters of the IR by the NSGA‐II algorithm. The simulated and experimental results illustrate the effectiveness of the methodology presented in this paper, which provides an alternative to the identification of IR dynamic parameters.

A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform

Abstract This investigation explores the analytical solutions to the time-fractional multi-dimensional Navier–Stokes (NS) problem using advanced approaches, namely the Aboodh residual power series method and the Aboodh transform iteration method, within the context of the Caputo operator. The NS equation governs the motion of fluid flow and is essential in fluid dynamics, engineering, and atmospheric sciences. Given the equation’s extensive and diverse applicability across several disciplines, we are motivated to conduct a thorough analysis to understand the complex dynamics associated with the nonlinear events it describes. For this purpose, we effectively handle the challenges posed by fractional derivatives by utilizing the Aboodh approach. This will enable us to obtain accurate analytical approximations for the time fractional multi-dimensional NS equation. By conducting thorough analysis and computational simulations, we provide evidence of the efficiency and dependability of the suggested methodologies in accurately representing the dynamic behavior of fractional fluid flow systems. This work enhances our comprehension of the utilization of fractional calculus in fluid dynamics and provides valuable analytical instruments for examining intricate flow phenomena. Its interdisciplinary nature ensures that the findings are applicable to various scientific and engineering fields, making the research highly versatile and impactful.