Behavior Of Dynamical Systems Research Articles

Towards accelerating particle‐resolved direct numerical simulation with neural operators

AbstractWe present our ongoing work aimed at accelerating a particle‐resolved direct numerical simulation model designed to study aerosol–cloud–turbulence interactions. The dynamical model consists of two main components—a set of fluid dynamics equations for air velocity, temperature, and humidity, coupled with a set of equations for particle (i.e., cloud droplet) tracing. Rather than attempting to replace the original numerical solution method in its entirety with a machine learning (ML) method, we consider developing a hybrid approach. We exploit the potential of neural operator learning to yield fast and accurate surrogate models and, in this study, develop such surrogates for the velocity and vorticity fields. We discuss results from numerical experiments designed to assess the performance of ML architectures under consideration as well as their suitability for capturing the behavior of relevant dynamical systems.

Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors

In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation.

Uncoupling of Damped Linear Potential Multi-degree-of-freedom Structural and Mechanical Systems

Abstract This paper provides the necessary and sufficient conditions for a multi-degree-of-freedom linear potential system with an arbitrary damping matrix to be uncoupled into independent subsystems of at most two degrees-of-freedom using a real orthogonal transformation. The incorporation of additional information about the matrices, which many structural and mechanical systems commonly possess, shows a reduction in the number of these conditions to three. Several new results are obtained and are illustrated through examples. A useful general form for the damping matrix is developed that guarantees uncoupling of such systems when they satisfy just two conditions. The results provided herein lead to new physical insights into the dynamical behavior of potential systems with general damping matrices and to robust computational procedures. It is shown that the dynamics of a damped potential system in which the damping matrix may be arbitrary is identical to that of a damped gyroscopic potential system with a symmetric damping matrix. This brings, for the first time, these two systems, which are seen today as belonging to different categories of dynamical systems, under a unified framework.

Simulation and experimental study of grid-connected photovoltaic power plants in a hot desert climate with fixed and dual-axis tracking

ABSTRACT This paper presents a comprehensive investigation into the performance of grid-connected photovoltaic (PV) power plants situated in a hot desert climate. The study employs a combination of simulation models and experimental data to assess the impact of two tracking systems – fixed and dual-axis – on the overall efficiency and energy yield of the PV installations. Through detailed simulations, we analyze the dynamic behavior of the PV systems under varying solar irradiance and the atmospheric conditions typical of hot desert environments. The dual-axis tracking system is compared against the conventional fixed-mount system to evaluate its effectiveness in maximizing energy production and improving the overall efficiency of the PV power plants. Experimental data collected from an actual grid-connected PV facility in a hot desert region is incorporated to validate the simulation results and enhance the accuracy of the study. The observed performance metrics include energy output, system reliability, and the impact of environmental factors on long-term sustainability. In general, in all weather conditions, solar tracking provides better yields than a fixed solar module, generating about 32% and 12% more energy in sunny and overcast weather conditions, respectively. Under sunny weather, the two-axis sun tracking system and a fixed tilt angle produce 333.228 kWh and 247.56 kWh of energy, respectively. The energy yield generated on a partly cloudy day by a two-axis sun tracking system and a fixed tilt angle PV system is 281.496 kWh and 257.856 kWh, respectively. In addition, the highest electricity gain for two-axis solar trackers versus fixed PV plants was found to be 34.6%, and the lowest value was found to be 9.16%. The experimental analysis shows that the efficiency of the polycrystalline PV module is 12% and 14% on sunny days and cloudy days, respectively. The comparison between fixed and dual-axis tracking systems contributes to the optimization of PV installations, enabling more informed decisions for sustainable energy production in regions characterized by high temperatures and intense solar radiation. To support the expanding applications of grid-tied PV systems with a sun tracker in the same or comparable location and climate conditions (Saharan environment), these studies have the practical utility of advising and offering helpful feedback to engineers, system designers, contractors, and investors.

Mixed-mode oscillations in a three-timescale coupled Morris-Lecar system.

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris-Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

Analyzing the effects of polymeric dielectric materials on micro capacitive pressure sensors: A model incorporating displacement-dependent porosity

Recently, the extensive utilization of porous polymeric materials to amplify the sensitivity of capacitive devices is noticeable. The absence of an effective mathematical model for studying these devices has spurred the development of a comprehensive mathematical model in the current work. This model is formulated to analyze the static and dynamic behavior of systems incorporating a porous polymer dielectric material within the gap between flexible and fixed microplates. The derived nonlinear governing equations encompass the effects of electrostatic force, von-Karman nonlinear strains, and displacement-dependent porosity. Employing spatial decomposition, the resulting nonlinear algebraic equations and ordinary differential equations are leveraged to study the static and transient dynamic behavior, as well as the frequency response of the sensor using a learning approach. Two scenarios are investigated to assess the impact of various geometrical and physical parameters on sensor sensitivity one with a polymeric material and another without, each with distinct parameter values. The results reveal that the inclusion of a polymeric dielectric material increases electrostatic force but concurrently elevates the equivalent stiffness of the structure. The effectiveness of using a polymeric dielectric material is contingent upon the specific geometrical and physical properties of the sensor. Moreover, the obtained results in simplified cases are compared to existing numerical and experimental data, demonstrating a high degree of agreement. This work significantly contributes to advancing the understanding of sensors incorporating porous polymer dielectric materials and underscores their potential for enhanced sensitivity across diverse applications.

Accelerated time history iteration method for offline real‐time hybrid testing

AbstractReal‐time hybrid testing (RTHT) is an efficient method to simulate the dynamic behavior of complex engineering systems. A novel offline RTHT method has been developed in recent years, wherein the computation of the numerical substructure and the loading of the experimental substructure are independent. Offline RTHT has obvious advantages in terms of accuracy, stability, and cost compared with conventional online RTHT. However, due to the excessive number of iterations, the application range of the existing offline RTHT methods is limited. This paper proposes an accelerated time history iteration (ATHI) method based on system identification and virtual iteration. A two‐loop parameter optimization (TLPO) method is developed to obtain an accurate discrete transfer function. Virtual iterations are performed by replacing the real system with an identified transfer function, which can reduce the number of real iterations. Physical tests were performed on structures equipped with a tuned mass damper or active mass damper, where resonance, nonlinearity, closed‐loop control, and measurement noise exist. The test results suggest that the real system can be accurately represented by the identified transfer function when adopting the TLPO method. The proposed ATHI successfully accelerates the convergence process while ensuring stability and accuracy.

Utilizing data-driven algorithms for blind modal parameter identification of structures from output-only video measurements

In structural dynamics and vibration analysis, modal identification plays a pivotal role in understanding and characterizing the dynamic behavior of complex systems. Traditional modal analysis techniques heavily rely on accurate sensor placement and knowledge of the excitation forces, which may not always be feasible or practical in real-world scenarios. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using computer vision techniques have gained much importance. But these methods need to know ahead of time where the structure's natural frequency ranges are, and they use steerable pyramids, which are complicated multi-scale image decomposition filters. To address these issues, a blind modal identification technique is suggested to extract the modal parameters (modal frequency and mode shapes) from the recorded structural vibration video signal. The proposed algorithm for unsupervised machine learning is the Non-Negative Matrix Factorization (NNMF) method, which is combined with the Generalized Complexity Pursuit (GCP) method for blind source separation. The NNMF algorithm is directly applied to the raw pixel-time series made from the video data to get the temporal components, which are then separated using GCP to find the individual modal frequencies and mode shapes. The above algorithm is first validated on a numerical model and then implemented on laboratory scale models (cantilever, single-degree, and multi-degree frame models). Finally, the proposed methodology is implemented on real-world recorded structural vibration videos to determine its noise sensitivity, such as the Tacoma Narrows bridge and the London Millennium footbridge. The modal parameters extracted are compared with those from the available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural vibration monitoring by identifying and reproducing complex vibration modes.

AI-Driven Virtual Sensors for Real-Time Dynamic Analysis of Mechanisms: A Feasibility Study

The measurement of the ground forces on a real structure or mechanism in operation can be time-consuming and expensive, particularly when production cannot be halted to install sensors. In cases in which disassembling the parts of the system to accommodate sensor installation is neither feasible nor desirable, observing the structure or mechanism in operation and quickly deducing its force trends would facilitate monitoring activities in industrial processes. This opportunity is gradually becoming a reality thanks to the coupling of artificial intelligence (AI) with design techniques such as the finite element and multi-body methods. Properly trained inferential models could make it possible to study the dynamic behavior of real systems and mechanisms in operation simply by observing them in real time through a camera, and they could become valuable tools for investigation during the operation of machinery and devices without the use of additional sensors, which are difficult to use and install. In this paper, the idea presented is developed and applied to a simple mechanism for which the reaction forces during operating conditions are to be determined. This paper explores the implementation of an innovative vision-based virtual sensor that, through data-driven training, is able to emulate traditional sensing solutions for the estimation of reaction forces. The virtual sensor and relative inferential model is validated in a scenario as close to the real world as possible, taking into account interfering inputs that add to the measurement uncertainty, as in a real-world measurement scenario. The results indicate that the proposed model has great robustness and accuracy, as evidenced by the low RMSE values in predicting the reaction forces. This demonstrates the model’s effectiveness in reproducing real-world scenarios, highlighting its potential in the real-time estimation of ground reaction forces in industrial settings. The success of this vision-based virtual sensor model opens new avenues for more robust, accurate, and cost-effective solutions for force estimation, addressing the challenges of uncertainty and the limitations of physical sensor deployment.

Adaptive fuzzy filtering for multi-area power systems subject to nonhomogeneous sojourn probabilities

This paper focuses on the design of an adaptive fuzzy filter for discrete-time multi-area power systems, considering the presence of sojourn probabilities and deception attacks. To capture the dynamic behavior of multi-area power systems more accurately, an innovative switching law is introduced, incorporating nonhomogeneous sojourn probability information. The feedback sojourn probability information is determined by a deterministic switched signal, enhancing the system's stability and performance. With the aim of addressing the potential impact of measurement outlier, a robust filter is developed, incorporating a dynamic saturation constraint and fuzzy logic systems. The filter effectively mitigates the influence of outliers by adaptively adjusting the saturation level based on estimation errors. The stability analysis is carried out using Lyapunov theory and average dwell-time information, demonstrating the mean square exponentially ultimately bounded of the augmented system. To validate the proposed algorithm, a simulation example is presented, showcasing its effectiveness and practical applicability in real-world scenarios.

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.

Exploring the Effect of Relaxation Time, Natural Surfactant, and Potential Determining Ions (Ca2+, Mg2+, and SO42−) on the Dynamic Interfacial Tension Behavior of Model Oil-Brine Systems

This study examined how the concentration of asphaltene and divalent ions in various salinities affects the interfacial tension (IFT) between a model oil/brine using the pendant drop method. The oleic phase consisted of a mixture of toluene and n-heptane (heptol), to which asphaltene was added to investigate how asphaltene molecules affect the surface properties. The base fluid was prepared with a salinity of 40,000 ppm, and two additional solutions with concentrations of 4000 ppm (low salinity) and 80,000 ppm (high salinity) were created. The results revealed that increasing the concentration of asphaltene within certain salinity ranges led to a decrease in IFT. The lowest IFT was observed at the 40,000 ppm salinity level, indicating that at this optimal salinity, the maximum asphaltene concentration migrated to the heptol/brine interface, reducing the IFT from 23 mN/m to 16 mN/m. Additionally, a 0.5 % wt of asphaltene demonstrated a significant concentration of micellization of natural surfactants, suggesting that the interface was nearly saturated with asphaltene. Consequently, concentrations higher than this value did not significantly alter the IFT. In the final part of the study, the impact of divalent ions was investigated, revealing that as the concentration of Ca2+ ions increased up to fourfold, the IFT decreased to 15 mN/m, about 10 % less than the base case. This value represented the lowest IFT compared to Mg2+ and SO42−. Moreover, modeling the results indicated that the relaxation time decreased with increasing salinity, suggesting that higher salinity accelerated the process of asphaltene absorption at the interface.

Quantum reaction-limited reaction–diffusion dynamics of noninteracting Bose gases

We investigate quantum reaction–diffusion (RD) systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ( A+A→∅ ) and coagulation ( A+A→A ) of particles at distance d. We consider the reaction-limited regime, where dissipative reactions take place at a rate that is small compared to that of coherent hopping. In classical RD systems, this regime is correctly captured by the mean-field approximation. In quantum RD systems, for noninteracting fermionic systems, the reaction-limited regime recently attracted considerable attention because it has been shown to give universal power law decay beyond mean field for the density of particles as a function of time. Here, we address the question whether such universal behavior is present also in the case of the noninteracting Bose gas. We show that beyond mean-field density decay for bosons is possible only for reactions that allow for destructive interference of different decay channels. Furthermore, we study an absorbing-state phase transition induced by the competition between branching A→A+A , decay A→∅ and coagulation A+A→A . We find a stationary phase-diagram, where a first and a second-order transition line meet at a bicritical point which is described by tricritical directed percolation. These results show that quantum statistics significantly impact on both the stationary and the dynamical universal behavior of quantum RD systems.

Analysis and modeling of forced-damped vibrations and their applications in medicine

Forced-damped vibrations are pivotal in various medical applications, significantly contributing to the examination of tissue mechanical properties, development of medical devices, and understanding of biological systems’ complexities. These vibrations represent the dynamic behavior of systems subjected to external forces and damping, where an external force continues to act, and damping determines the rate of energy dissipation. Advanced exploration of damping properties has led to the creation of novel technologies and methods, enhancing our ability to probe and manipulate the complex mechanical dynamics of biological tissues.

Dynamics of Quadratic Volterra-Type Stochastic Operators Corresponding to Strange Tournaments

By studying the dynamics of these operators on the simplex, focusing on the presence of an interior fixed point, we investigate the conditions under which the operators exhibit nonergodic behavior. Through rigorous analysis and numerical simulations, we demonstrate that certain parameter regimes lead to nonergodicity, characterized by the convergence of initial distributions to a limited subset of the simplex. Our findings shed light on the intricate dynamics of quadratic stochastic operators with interior fixed points and provide insights into the emergence of nonergodic behavior in complex dynamical systems. Also, the nonergodicity of quadratic stochastic operators of Volterra type with an interior fixed point defined in a simplex introduces additional complexity to the already intricate dynamics of such systems. In this context, the presence of an interior fixed point within the simplex further complicates the exploration of the state space and convergence properties of the operator. In this paper, we give sufficiency and necessary conditions for the existence of strange tournaments. Also, we prove the nonergodicity of quadratic stochastic operators of Volterra type with an interior fixed point, defined in a simplex.

Learning the Topology and Behavior of Discrete Dynamical Systems

Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to certain classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known Natarajan dimension formalism. Our results provide a theoretical foundation for learning both the topology and behavior of discrete dynamical systems.

Automated State Estimation for Summarizing the Dynamics of Complex Urban Systems Using Representation Learning

Complex urban systems can be difficult to monitor, diagnose and manage because the complete states of such systems are only partially observable with sensors. State estimation techniques can be used to determine the underlying dynamic behavior of such complex systems with their highly non-linear processes and external time-variant influences. States can be estimated by clustering observed sensor readings. However, clustering performance degrades as the number of sensors and readings (i.e. feature dimension) increases. To address this problem, we propose a framework that learns a feature-centric lower dimensional representation of data for clustering to support analysis of system dynamics. We propose Unsupervised Feature Attention with Compact Representation (UFACR) to rank features contributing to a cluster assignment. These weighted features are then used to learn a reduced-dimension temporal representation of the data with a deep-learning model. The resulting low-dimensional representation can be effectively clustered into states. UFACR is evaluated on real-world and synthetic wastewater treatment plant data sets, and feature ranking outcomes were validated by Wastewater treatment domain experts. Our quantitative and qualitative experimental analyses demonstrate the effectiveness of UFACR for uncovering system dynamics in an automated and unsupervised manner to offer guidance to wastewater engineers to enhance industrial productivity and treatment efficiency.

Dynamic analysis on an asymmetric spatial dumbbell-type model

The structural symmetric breaking of the spatial structure will enhance the coupling dynamic behaviors and bring new challenges for the dynamic analysis on the spatial structure inevitably. The main contribution of this paper is proposing a structure-preserving iteration method to investigate the effects of the dynamic symmetry-breaking factors on the dynamic behaviors of the rigid-flexible coupling systems. Firstly, the spatial flexible damping beam assembled with two particles on both ends is simplified as an asymmetric spatial dumbbell-type model. For this model, the coupling dynamic equations are presented based on the Hamiltonian variational principle. Then, connecting the symplectic precise integration method for the ordinary differential equations mainly controlling the plane motion of the model and the generalized multi-symplectic scheme for the partial differential equation mainly controlling the transverse vibration of the beam, a structure-preserving numerical iteration method is proposed, which provides a new way to analysis the dynamic behaviors of the coupling problems with the symmetric breaking. Finally, the effects of the absolute mass and the mass ratio of the additional particles on the orbit radius, the orbit true anomaly velocity, the attitude angle velocity of the model and the transverse vibration of the flexible beam are reproduced by using the structure-preserving numerical iteration method in the numerical simulations. Particularly, the effects of the additional particles on the attitude stability of the model and the vibration dissipation of the flexible damping beam are investigated, which gives some guidance for the attitude adjustment strategy and the vibration control method for the spatial flexible structure with the structural symmetric breaking.

ELViM: Exploring Biomolecular Energy Landscapes through Multidimensional Visualization.

Molecular dynamics (MD) simulations provide a powerful means of exploring the dynamic behavior of biomolecular systems at the atomic level. However, analyzing the vast data sets generated by MD simulations poses significant challenges. This article discusses the energy landscape visualization method (ELViM), a multidimensional reduction technique inspired by the energy landscape theory. ELViM transcends one-dimensional representations, offering a comprehensive analysis of the effective conformational phase space without the need for predefined reaction coordinates. We apply the ELViM to study the folding landscape of the antimicrobial peptide Polybia-MP1, showcasing its versatility in capturing complex biomolecular dynamics. Using dissimilarity matrices and a force-scheme approach, the ELViM provides intuitive visualizations, revealing structural correlations and local conformational signatures. The method is demonstrated to be adaptable, robust, and applicable to various biomolecular systems.

Bifurcation Regulations Induced by Joint Noise in a Tri-Rhythmic Van Der Pol System

Tri-rhythmical nature has attracted extensive attention from scholars in describing the dynamical behaviors of self-sustained systems. In this paper, we consider a tri-rhythmic van der Pol system and give a bifurcation analysis of a stochastic tri-rhythmic self-sustained system under joint noise perturbation. Based on an approximate approach, we give the stationary probability density function of amplitudes, and we find that the noise and time-delay feedback, regulating the velocity time-delay feedback strength parameter, may not cause transitions among unimodal, bimodal and trimodal in the tri-rhythmic system. More stochastic bifurcations appear by regulating the time delay in this system. The system, surprisingly, undergoes five times of stochastic bifurcations when the time delay is monotonically increased. It is shown that the time delay is more sensitive to the tri-rhythmic system and a much stronger dependence on the system. From a biological point of view, the reaction rate of biological molecules can be enhanced or diminished by the change of the noise intensity or correlation time of Gaussian colored noise. More surprisingly, an increase in displacement feedback will delay the reaction rate; however, the effect of an increase in velocity feedback on the reaction rate depends on the time delay. A detailed research on the parameter space indicates that time delay and colored noise parameters can effectively control the multirhythmicity of the system. Finally, this paper verifies the effectiveness of the theoretical solution through the numerical results of Monte Carlo simulation of the original system. These results may help to further explore forking bifurcations in real-world applications. This research provides new insight into the understanding of nontrivial effects of joint noise on the tri-rhythmic system.