Dynamic Behaviour Of System Research Articles

Update (3.0) to LyapXool: Quadratic programming

This is an update to PII: S2352711020303290, LyapXool is a C＋＋ program to compute complete Lyapunov functions and their orbital derivatives for any dynamical system expressed by an autonomous ordinary differential equation. New methods and improvements made in the third version are discussed. In particular, the computation of complete Lyapunov functions within quadratic programming methods are now computed by the software. These new approaches can be used to better analyse the behaviour of dynamical systems expressed as systems of autonomous equations. The structure of the program is object-oriented rather than procedural and the output formatting has been restructured to make it easier to understand. The program maintains its user friendliness. This paper describes how the code is organised, how it can be used to compute complete Lyapunov functions and their subsequent properties for dynamical systems, and it provides an interesting example of its application.

Strange nonchaotic attractors and bifurcation of a four-wheel-steering vehicle system with driver steering control

In this paper, a dynamical model is developed for the four-wheel-steering(4WS)vehicles, with nonlinear lateral tyre forces and quasi-periodic disturbances from the steering mechanism and quasi-periodic pavement external deformation. Initially, the stability and Hopf bifurcation of the 4WS vehicle system without disturbance are analyzed employing the central manifold theory and projection method. The effects of parameters on the stability and the types of Hopf bifurcation for the vehicle system are also discussed. It is shown that both Hopf bifurcation and degenerate Hopf bifurcation occur in the vehicle system. The critical speed decreases with increased driver’s perceptual time delay and distance from the vehicle’s center of gravity to the front axles, while it increases with the control strategy coefficient. However, the increase of the frontal visibility distance of the driver leads to an initial increase of the critical speed, decreasing afterwards. Subsequently, the strange nonchaotic dynamical behaviour of the disturbed 4WS system is investigated. Several routes and mechanisms for the birth of strange nonchaotic attractors (SNAs) are identified, including the torus doubling bifurcation, the torus fractalization, and the loss of transverse stability of a torus. Finally, the nonchaotic property is verified through the calculation of the maximum Lyapunov exponent, and the strange property is characterized using power spectra and rational approximation.

Some Aspects of the Effects of Dry Friction Discontinuities on the Behaviour of Dynamic Systems

Most studies in the literature consider the value of the coefficient of dynamic friction to be constant. We studied the evolution of a dynamic system when the coefficient of friction results in different values depending on the contact surfaces. A system with four balls fixed on an aluminium plate was driven with constant velocity into motion on the coaxial races of two identical outer bearing rings. The assembly presents a motion with periodic variable amplitude between two extremes, a fact that suggests the presence of a periodical excitation. The test was repeated, but this time, new bodies were used, which were two identical bodies made of two balls rigidised via a short cylindrical rod. When the rings were driven into rotational motion, the two bodies performed different motions; if the bodies were inter-changed, the differences between the motions remained. The rings were analysed, and a small region on the race of one ring was observed, where the roughness was considerably greater than the rest of the surface. Then, a mathematical model for the dynamic system with different friction coefficients was proposed and solved. This model is capable of simulating different situations, such as oscillatory motion and circular motion, with or without separation of the contacting bodies. Here, we present a dynamic model with Hertzian contact points in the presence of dry friction, with the coefficient of friction changing suddenly on the contacting surfaces.

Dynamical Behaviour of a Predator-Prey System with Holling Type III Functional Response under Harvesting and Self-crowding

Dynamical Behaviour of a Predator-Prey System with Holling Type III Functional Response under Harvesting and Self-crowding

Combined effect of track-bridge interaction on the dynamic response of a simply supported railway bridge

In this work, the objective is to understand the effect of the nonlinear behaviour of the ballasted track, or the mechanism of vertical and horizontal track-bridge interaction behaviour, on the dynamic response of a simply supported railway bridge, carrying a single ballasted track characterized by a fractional order viscoelastic nonlinear Winkler foundation type, and acted by a moving train load with constant speed. The main feature of the model is that the horizontal and vertical interactions at the interface between the bridge deck and the ballasted track, composed by rails, sleepers and ballast, is introduced through a nonlinear cubic force-displacement relation, schematizing the nonlinear stiffness, plus fractional derivative term for simulating the rail bed’s damping behaviour and a system of horizontally orientated spring-damper elements. By applying the two numerical methods, fourth-order Runge-Kutta method and Finite Difference Method, the validation of the dynamic behaviour of the rail-bridge system is performed, and numerical simulations demonstrate the accuracy of the proposed theoretical model for predicting the real behaviour of the studied bridge taking into account the track-bridge interaction effect. The influence of the fractional-order derivative and the distance between sleepers on the critical velocities, associated with resonance effects, is also addressed.

Analytical Description of the Dynamic Behaviour of the Passive Battery Supercapacitor Hybrid System

Analytical Description of the Dynamic Behaviour of the Passive Battery Supercapacitor Hybrid System

Dynamical behaviour and meta heuristic optimization of a hospital management software system

The growing demand for easily available healthcare in recent years has fuelled the digitization of healthcare services. The Hospital Management System (HMS) software stands out as a comprehensive solution among the software systems and tools that hospitals and clinics are developing in tandem with this trend. In order to effectively manage many facets of hospital operations, in this paper, we propose an approach for investigating software of this kind. Thus, we characterise the HMS software as a unique sort of batch arrival retrial queueing system (QS) that can handle both ordinary and priority patient demands. Furthermore, it permits patient resistance (balk) and departure (renege) in specific circumstances. The proposed model is additionally deployed within the framework of Bernoulli working vacation. The supplementary variable technique (SVT) has been utilised to obtain the necessary results. ANFIS, a soft computing tool, is used to validate the analytical results as well. Finally, this study seeks to enhance the cost-effectiveness of software creation by employing four unique optimization methods, aiming to achieve optimal efficiency in resource utilization.

Product Development Methodology Targeting Efficiency and Acoustics of E-Mobility Gearboxes

This paper presents an approach for physical/virtual coupled product development and validation. A method for studying the influence of tooth geometry on the efficiency and acoustics of an electric vehicle’s powertrain will be presented. To achieve improved acoustic characteristics the micro geometry of the teeth will be optimized. The modified gears were analysed on a gear test rig under load and at high speeds and evaluated with regard to their acoustic properties. Established analytical models are used to describe the influence of profile modifications on the gear stiffness of helical gears. The authors’ approach is to calculate the dynamic system behaviour of the gearbox using a 1D simulation. Based on this, studies of the entire gear box will be performed. For this, the results of the 1D simulation are coupled with 3D FEA analyses. This enables acoustic calculations (structure-borne and airborne sound) to be carried out.

DYNAMIC MODELLING OF THREE-PHASE MICROGRIDS INCLUDING DQ0 CURRENT CONTROLLED PHOTOVOLTAIC GENERATION UNDER TRANSIENT CONDITIONS

ABSTRACT: The photovoltaic generation can be interconnected to power systems or to insulated grids to satisfy the growing electrical demand as an alternative renewable energy source. The photovoltaic generator dynamics affects the control, protection, stability, and power quality of the electrical grid, this network dynamics requires to be examined and conveniently regulated and adjusted. The dynamic averaged model for the dq0 current controlled DC/AC inverter is applied to obtain the time-domain response to electromagnetic transients under special conditions such as electrical load fluctuations, unbalanced faults, voltage and current transients to verify e.g., the ride through capability or to adjust the protection and control devices, these transients can be present during the operation of electrical microgrids and power systems interconnected with photovoltaic generation. The system modelling includes the photovoltaic plant interconnected with the microgrid using the dq0 current controlled DC/AC inverter. The case studies are applied to analyse three-phase electrical microgrids, their time-domain response, and the obtained voltage and current waveforms can be used to verify the dynamic behaviour and stability of the electrical system interconnected with photovoltaic generation and similarly to verify the operation of the dq0 current controller for the inverter. The results can be used to control the microgrid dynamic behaviour. Keywords: current control, dq0 transform, inverter, microgrids, photovoltaic generation, power quality, protection, time-domain, transients, unbalanced faults, unbalanced voltage sags, voltage source converter

Shaping closed-loop supply chain dynamics: Mitigating the bullwhip effect and improving customer satisfaction in production systems with material reuse

Modern societies are currently transitioning towards more circular economic models to reduce environmental impacts and leverage economic opportunities. Managing the emerging supply chains, more complex and uncertain, poses a considerable challenge for many organisations. This work examines the dynamic behaviour of these closed-loop systems under different replenishment policies and varying levels of product returns and lead times. We model a generalised multi-level, closed-loop supply chain of a production system with material reuse, drawing inspiration from the real-world operations of cider makers in Spain. We investigate its ability to effectively and efficiently satisfy the consumer through four performance metrics: fill rate, bullwhip ratio, inventory cover, and reuse demand share. Through experimentation techniques, we observe that the highest performance is generally obtained when the retailer applies a pure pull policy while the manufacturer adopts a level scheduling policy. This strategy, built on lean principles, can achieve much lower operational costs while providing similar, or even better, service levels compared to more popular and complex alternatives. Based on our findings, we provide a set of actionable managerial implications that would help supply chain professionals successfully implement and manage these supply chains.

Dynamic amplification of rail tracks in high-speed lines: Exploring train effects and impact of ground treatment

When the train circulation speed is much lower than the critical speed of the track-ground system, problems with dynamic amplification effects are purely theoretical. However, the situation can change if a new high-speed line, with a higher operation speed, is planned for a site with soft soils. In such cases, it may be necessary to assess the importance and consequences of the critical speed phenomenon on safety and operational costs of the railway track. A practical measure involving the ground treatment may contribute to an improvement of the system behaviour. This measure is based on replacing a portion of the natural soil with stiffer materials or by employing grouting. The current paper provides numerical evidence as the soil reinforcement significantly improves the dynamic behaviour of the ground-track system. It is also possible to conclude that localized ground reinforcement below the track yields a response similar to extending the reinforcement over a larger area. This conclusion is particularly interesting for engineering practice and for numerical/semi-analytical analysis. The study of the effect of the train geometry on the critical speeds of the train-track system is also carried out. However, the main conclusion is that the definition of the critical speed as the value that induces larger amplification due to the passage of a single load is a conservative approach. Finally, it was observed that an approach based on the calculation of the dispersion curves enhances an adequate estimation of the system’s critical speed.

Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package

We propose a parallel (distributed) version of the spectral proper orthogonal decomposition (SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the dataset preserving time. This approach is adopted to preserve the non-distributed fast Fourier transform of the data in time, thereby avoiding the associated bottlenecks. The parallel SPOD algorithm is implemented in the PySPOD library and makes use of the standard message passing interface (MPI) library, implemented in Python via mpi4py. An extensive performance evaluation of the parallel package is provided, including strong and weak scalability analyses. The open-source library allows the analysis of large datasets of interest across the scientific community. Here, we present applications in fluid dynamics and geophysics, that are extremely difficult (if not impossible) to achieve without a parallel algorithm. This work opens the path toward modal analyses of big quasi-stationary data, helping to uncover new unexplored spatio-temporal patterns. Program summaryProgram Title: PySPODCPC Library link to program files:https://doi.org/10.17632/jf5bf26jcj.1Developer's repository link:https://github.com/MathEXLab/PySPODLicensing provisions: MIT LicenseProgramming language: PythonNature of problem: Large spatio-temporal datasets may contain coherent patterns that can be leveraged to better understand, model, and possibly predict the behavior of complex dynamical systems. To this end, modal decomposition methods, such as the proper orthogonal decomposition (POD) and its spectral counterpart (SPOD), constitute powerful tools. The SPOD algorithm allows the systematic identification of space-time coherent patterns. This can be used to understand better the physics of the process of interest, and provide a path for mathematical modeling, including reduced order modeling. The SPOD algorithm has been successfully applied to fluid dynamics, geophysics and other domains. However, the existing open-source implementations are serial, and they prevent running on the increasingly large datasets that are becoming available, especially in computational physics. The inability to analyze via SPOD large dataset in turn prevents unlocking novel mechanisms and dynamical behaviors in complex systems.Solution method: We provide an open-source parallel (MPI distributed) code, namely PySPOD, that is able to run on large datasets (the ones considered in the present paper reach about 200 Terabytes). The code is built on the previous serial open-source code PySPOD that was published in https://joss.theoj.org/papers/10.21105/joss.02862.pdf. The new parallel implementation is able to scale on several nodes (we show both weak and strong scalability) and solve some of the bottlenecks that are commonly found at the I/O stage. The current parallel code allows running on datasets that was not easy or possible to analyze with serial SPOD algorithms, hence providing a path towards unlocking novel findings in computational physics.Additional comments including restrictions and unusual features: The code comes with a set of built-in postprocessing tools, for visualizing the results. It also comes with extensive continuous integration, documentation, and tutorials, as well as a dedicated website in addition to the associated GiHub repository. Within the package we also provide a parallel implementation of the proper orthogonal decomposition (POD), that leverages the I/O parallel capabilities of the SPOD algorithm.

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.

Long-term effect of SARS-CoV-2 variant : Challenging issues and controlling strategies

In this study, a latest version of COVID-19 pandemic is hand overed. A Stochastic post COVID-19 delayed model is developed to explore the spread of COVID-19 as well as omicron variant with the correlation of heart attack. This article provides an eradication of the COVID-19 and omicron variant as well as the population who have heart attack after post COVID-19 of these epidemic diseases. Then the existence and uniqueness of global positive solution are studied. Ensuing, In this article, we classify COVID-19 virus and omicron variant which go to extinction and become persistent in mean. By using Lyapunov function, the existence of ergodic stationary distribution are established. Later from the persistent disease as well as extinction, heart disease are ready to develop in the human body. By Eventually, an optimal control strategies are introduced in the form of stochastic post COVID-19 delayed model to control two different types of virus. Finally, the numerical simulation are presented to determine the behavior of dynamical system by utilizing the real data of United Kingdom.

Identification of natural frequencies of machine tools during milling: comparison of the experimental modal analysis and the operational modal analysis

Modal parameters (natural frequencies, mode shapes and modal damping) help to understand the dynamic behaviour of complex systems like machine tools. There are several approaches for finding the modal parameters. The Experimental Modal Analysis (EMA) has proven to be effective at standstill of a machine tool. The excitation, realized with impulse hammer or shaker, and excited responses at several locations are measured. Alternatively, the Operational Modal Analysis (OMA) can be deployed for finding the modal parameters during operation. Here, responses to excitation resulting from operation are only measured. The modal parameters are mathematically identified from the measured signals in both cases but with different methods. This paper discusses, to what extent both approaches (EMA and OMA) can lead to plausible identification of natural frequencies of a machine tool during milling. Concerning the EMA, attention is paid to capturing the excitation. Process forces can be assumed to be the most significant excitation. However, there are other excitation sources beside the process forces (e.g. drives, hydraulic and pneumatic aggregates), which are considered by this assumption to be a part of disturbances with consequence for the identification of the modal parameters. Regarding the OMA, attention is paid to the fact that the excitation is assumed to be broadband like the white noise. Unfortunately, this assumption does not match the characteristics of a real excitation. This paper contains the identification of natural frequencies of a machine tool during milling within both approaches. The achieved results are compared and discussed.

Dynamics and scaling of internally cooled convection

Our goal is to investigate fundamental properties of the system of internally cooled convection. The system consists of an upward thermal flux at the lower boundary, a mean temperature lapse-rate and a constant cooling term in the bulk with the bulk cooling in thermal equilibrium with the input heat flux. This simple model represents idealised dry convection in the atmospheric boundary layer, where the cooling mimics the radiative cooling to space notably through longwave radiation. We perform linear stability analysis of the model for different values of the mean stratification to derive the critical forcing above which the fluid is convectively unstable to small perturbations. The dynamic behavior of the fluid system is described and the scaling of various important measured quantities such as the total vertical convective heat flux and the upward mass flux is measured. We introduce a lapse-rate dependent dimensionless Rayleigh-number Raγ that determines the behavior of the system, finding that the convective heat-flux and mass-flux scale approximately as Raγ0.5 and Raγ0.7 respectively. The area-fraction of the domain that is occupied by upward and downward moving fluid and the skewness of the vertical velocity are studied to understand the asymmetry inherent in the system. We conclude with a short discussion on the relevance to atmospheric convection and the scope for further investigations of atmospheric convection using similar simplified approaches.

Analyzing Small-Signal Stability in a Multi-Source Single-Area Power System with a Load-Frequency Controller Coordinated with a Photovoltaic System

The frequency deviation from the nominal working frequency in power systems is a consequence of the imbalance between total electrical loads and the aggregate power supplied by production units. The sensitivity of energy system frequency to both minor and major load variations underscore the need for effective frequency load control mechanisms. In this paper, frequency load control in single-area power system with multi-source energy is analysed and simulated. Also, the effect of the photovoltaic system on the frequency deviation changes in the energy system is shown. In the single area energy system, the dynamics of thermal turbine with reheat, thermal turbine without reheat and hydro turbine are considered. The simulation results using Simulink/Matlab and model analysis using eigenvalue analysis show the dynamic behaviour of the power system in response to changes in the load.

Quotient toposes of discrete dynamical systems

Lawvere's open problem on quotient toposes has been solved for boolean Grothendieck toposes but not for non-boolean toposes. As a simple and non-trivial example of a non-boolean topos, this paper provides a complete classification of the quotient toposes of the topos of discrete dynamical systems, which, in this context, are sets equipped with an endofunction. This paper also offers an order-theoretic framework to address the open problem, particularly useful for locally connected toposes.Our result is deeply related to monoid epimorphisms. At the end of this paper, utilizing the theory of lax epimorphisms in the 2-category Cat, we explain how (non-surjective) monoid epimorphisms from N correspond to (non-periodic) behaviors in discrete dynamical systems.

Enhancing the Intellectual Capital of Research and Development Centres using Business Intelligence: A System Dynamics Approach

AbstractThis study employs system dynamics simulation to examine the scenarios and policies aimed at enhancing the intellectual capital of R&D centres. Through an in‐depth review of the relevant literature, such as thematic analysis, along with an examination of regulations and expert interviews and focus group discussions as well, the dimensions, variables and measurement indicators associated with Intellectual Capital and Business Intelligence, were identified. The dynamic relationships among these variables are then modelled, and the model's behaviour is simulated. By implementing two scenarios, namely reducing government financial support and increasing the competitive environment, the simulation results indicate that the enhancement of informational and relational capital will improve structural capital and increase business intelligence. Over ten years of simulation, the centre's dedicated revenue will grow by more than 150%. The proposed dynamic modelling and system behaviour simulation can serve as a basis for setting an intellectual capital framework in R&D centres, particularly in developing countries.

On the prediction of the time-varying behaviour of dynamic systems by interpolating state-space models

In this article, a local Linear Parameter Varying (LPV) model identification approach is exploited to analyze the dynamic behaviour of a structure whose dynamics varies over time. This structure is composed by two aluminum crosses connected by a rubber mount. To observe time-dependent variations on the dynamics of this assembly, it is placed in a climate chamber and submitted to a six minute temperature run-up. During this run-up the structure is continuously excited by a shaker. The load provided by this device is measured by a load cell, while six accelerometers are measuring the responses of the system. The temperatures of the air inside the climate chamber and at the surface of the mount are also continuously measured. It is found that during the performed temperature run-up, the rubber mount temperature increased from, roughly, 14℃ to, approximately, 35.2℃. By using the measured load provided by the shaker and the measured accelerations, Frequency Response Functions (FRFs) at five different rubber mount temperatures are computed. From each of these sets of FRFs, state-space models are estimated. Afterwards, these models are used to define an interpolating LPV model, which enables the computation of interpolated state-space models representative of the dynamics of the system at each time sample. It is found that by feeding the interpolated state-space models with the measured load, an accurate simulation of the measured accelerations is obtained. Moreover, by exploiting a joint input-state estimation algorithm with the interpolated state-space models and with the measured accelerations, a very good prediction of the applied load can be obtained. It is also shown that if the time dependency of the dynamics of the system is ignored, the results are less accurate.