Properties Of Dynamical Systems Research Articles

High-order nonstandard finite difference methods preserving dynamical properties of one-dimensional dynamical systems

High-order nonstandard finite difference methods preserving dynamical properties of one-dimensional dynamical systems

Quantum model in the context of six-level atom and deformed Lie algebra: Entanglement and statistical properties

In this work, we study the interplay between an atomic system with six levels configured in a cascade-type and one-mode fields in the framework of the f-coherent states. We explore the considered system dynamic properties under the effects of field nonlinearity and the number of photon transitions. In particular, we consider the quantum coherence, atomic upper level-occupation probability, and atom–field entanglement of a system when the effect of deformation is considered. Moreover, we analyze the dynamic of the Mandel parameter as a quantifier of the statistical properties of the field in the presence of deformation when the field is initially in coherent states.

Why is economics the only discipline with so many curves going up and down? There is an alternative

Even the most rudimentary training from Economics 101 starts with demand curves going down and supply curves going up. They are so ‘natural’ that they sound even more obvious than the Euclidian postulates in mathematics. But are they? What do they actually mean? Start with “demand curves”. Are they hypothetical ‘psychological constructs’ on individual preferences? Propositions on aggregation over them? Reduced forms of actual dynamic proposition of time profiles of prices and demanded quantities? Similar considerations apply to “supply curves” The point here, drawing upon the chapter by Kirman and Dosi, in Dosi (Dosi, Foundations of Complex Evolving Economies Innovation, Organization and Industrial Dynamics, Oxford University Press, 2023), is that the forest of demand and supply curves is basically there to populate the analysis with double axiomatic notions of equilibria, both ‘in the head’ of individual agents, and in environments in which they operate. Supply and demand “curves”, I am arguing, are one of the three major methodological stumbling blocks on the way of progress in economics, the other related ones being ‘utility functions’ and ‘production functions’. There is an alternative: represent markets and industries how they actually works, and model them both via fully fledged Agent Based Models and via lower dimensional dynamical systems.

Dynamical Systems on Graph Limits and Their Symmetries

AbstractThe collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and the dynamics thereon. We elucidate the symmetry properties of dynamical systems on graph limits—including graphons and graphops—and analyze how the symmetry shapes the dynamics, for example through invariant subspaces. In addition to traditional symmetries, dynamics on graph limits can support generalized noninvertible symmetries. Moreover, as asymmetric networks can have symmetric limits, we note that one can expect to see ghosts of symmetries in the dynamics of large but finite asymmetric networks.

Dynamics of accelerating and decelerating flows: A boundary layer examination with non-similar approach and convective boundary condition

Moisture/air-flow over the aircraft wing and bonnet of a moving car in aerodynamical systems exhibit dynamic behavior characterized by accelerating and decelerating flows. These analysis is essential and applicable in various fields, including physics, engineering, and fluid mechanics. The present investigation aim to explore the dynamics of accelerating and decelerating flows within the framework of boundary layer examination. To achieve these objectives, a non-similar group of transformations is employed to convert the governing dimensional two-variable dynamical system into a dimensionless differential form, with η and ξ as the independent variables. To gain physical understanding of the mathematical equations governing the flow, an efficient bivariate spectral collocation method (BSCM) is employed for analyzing the flow dynamics. This method allows for a thorough investigation of the behavior and characteristics of the accelerating and decelerating Casson flows. Subject to the convergence and residual error analysis of the numerical results, the effects of pertinent parameters on the flow variables were investigated. The findings of this study show that the effects of flow parameters on decelerating and accelerating flows are not completely opposite. Additionally, the Biot parameter positively impacts the velocity and temperature profiles of the two dynamical flows. However, an increase in the Casson fluid parameter β has an opposing effect on the temperature and concentration profiles of both flows.

Small-signal simulation applied to calculation of the parameters of nonlinear dynamics processes control systems for DC/DC converters

The article discusses the issues of choosing the control system parameters for pulse-width DC/DC converters with the target-oriented control. This takes into account the nonlinear dynamic processes control system, which is important when constructing power conversion systems with increased requirements for speed. A nonlinear dynamic model of the system is developed taking fully into account the dynamic properties of the control system. A technique for selecting control system parameters based on small-signal modelling is proposed, which greatly simplifies the calculation process. The suggested approach can be applied in developing DC/DC converters of a wide class.

Dynamic property of a stochastic cooperative species system with distributed delays and Ornstein–Uhlenbeck process

Scanning the whole writing, we discuss a stochastic cooperative species system with distributed delays under the influences of Ornstein–Uhlenbeck process of mean regression. We successfully obtain the existence and uniqueness of positive solutions for stochastic system at first. Secondly, by studying the Lyapunov function, we present the existence of the stationary distribution of the system. We are relatively familiar with the understanding of the density function of random systems. This paper also gives the expression of the density function of the random system near the unique positive equilibrium. In addition, the asymptotic properties of the p-moment boundedness and solution of the stochastic population system are also studied. In particular, we use numerical simulation to verify the theoretical results in the last section.

Modification of rotor modal properties based on structural changes in the stiffness of its bearings and shaft

The rotor structures are fundamental mechanical systems that realize the transfer of rotary motion in technical devices and systems. In some operating regimes, the rotor systems are often subjected to undesirable and damaging phenomena resulting in resonant state. The ability to prevent or reduce the level of unwanted rotor vibrations in the given operating mode is an important task in the process of structural design of rotor structures. In general, the dynamic properties of rotor systems depend on their spatial properties - geometric parameters and material properties, i.e. distribution of mass and stiffness properties of rotor structures. For the structural design of the rotor or its structural modification, which will allow the redistribution of its spatial properties (mass and stiffness), two approaches based on changing the bearing stiffness and also on the shaft stiffness are presented in this paper. The main goal for modifying the spatial properties of the rotor is to get the critical rotor speed out of the operating speed range.

Simulation of Rarefied Gas Flow in a Channel Applying Artificial Neuron Network

The purpose of the present paper is to confirm numerically applying our ANN algorithm for transitional gas flow between continuum and free-molecular flow. The main advantage of this approach is substantial computing time economy compared to usual DSMC procedure. The learning of ANN is based on well known rarefied gas flow examples, analytic solutions in limit cases, calculations by lattice Boltzmann method (LBM), and on quite few Monte Carlo simulations. Our previous results obtained for large Knudsen numbers have been applied near the free-molecular regime. In this region the flow has demonstrated the properties of unstable nonlinear dynamic system. The flow of nitrogen in a microchannel with aspect ratio L/h = 20 and by pressure ratio P between 1.84 and 4.14 is simulated by ANN. This example has shown a good coincidence of ANN and DSMC calculations even in the case when only a small part of original DSMC computation has been applied for learning ANN. Thus, computing time is reduced up to 10 times in this case.

Modeling of flexible bevel gear rotor systems: Modal and dynamic characterization

Bevel gears, a crucial part of aircraft transmission systems, are more susceptible to wheel body vibration issues as lightweight requirements rise. In the past, the gear wheel body was often considered rigid while assessing the dynamic properties of gear systems. Constructing a bevel gear model with a thin-walled structure might not be appropriate for this modeling technique; this research suggests a dynamic model that considers the flexibility of bevel gears. The web and teeth structure of the gear are preserved by realistic modeling using three-dimensional hexahedral components. The component mode synthesis (CMS) approach reduces the model order for increased computational efficiency. To confirm the accuracy of the modeling method, the modal frequencies and vibration shapes of the proposed model single-gear shaft are compared with results from experiments and ABAQUS. By contrasting ABAQUS system-level meshing modal frequencies and vibration shapes, the accuracy of the system model assembly is further confirmed. The model examines the impact of bevel gear flexibility on the modal frequencies, modal vibration shapes, and system dynamic properties. The mode shape diagram at dangerous modal frequencies found using the modal strain energy technique and the vibration displacement cloud maps at resonance speeds computed using the Newmark-β method are mutually verified, and this demonstrates that lightweight bevel gears are more susceptible to excitation due to nodal diameter type vibrations. Proposed and traditional models anticipate substantially different resonance speeds since the traditional model assumes that the gear, being a rigid disk, can only excite the shaft's bending mode of vibration. The proposed model provides a more comprehensive description of the dynamic characteristics of bevel gear systems, providing a theoretical basis and optimization tool for the high-performance design, vibration reduction, and noise control of high-speed lightweight gear transmission systems.

Experimental Investigation to Evaluate the Dynamic Properties of a Scaled Rectangular Tuned Liquid Damper Using High-Speed Videos

The use of tuned liquid dampers (TLDs) as an alternative to reduce the response of flexible structures with a low amount of structural damping is a viable option. The correct characterization of the dynamic properties of the TLD plays an important role in the performance of the TLD-main structure system. This work presents the results of an experimental study to evaluate the dynamic properties of a scaled rectangular TLD using high-speed videos. For the experimental investigation, a scaled rectangular TLD is subjected to lateral displacement of the sinusoidal type with amplitudes that range from 5 to 40 mm and frequency equal to 0.625 Hz. The dynamic properties of the TLD system are identified with the use of high-speed videos with a duration of 28.96 s and recorded at 500 frames per second (fps). The recorded videos are analyzed with the software Tracker to extract time histories of wave elevation at predefined locations. The frequency and damping of the TLD system are identified from the time histories of wave elevation through Fourier analysis and free-vibration decay. The findings of this study revealed that the identified dynamic properties of the TLD by using high-speed videos presented small differences with respect to the target values, with errors that range from 0.93 to 2.9% for frequency and from 1.6 to 8.8% for damping, indicating that the use of high-speed videos can be an alternative to evaluate the dynamic properties of TLD systems.

Deep learning‐based response spectrum analysis method for building structures

AbstractThe response spectrum method has gained widespread acceptance in practical applications owing to its favorable compromise between accuracy and practical efficiency. The method predicts the peak responses of multi‐degree‐of‐freedom (MDOF) systems by combining modal responses. The Square Root of the Sum of Squares (SRSS) and Complete Quadratic Combination (CQC) rules are commonly used for modal combinations. However, it has been widely known that these rules have limitations in accurately predicting responses influenced by higher modes and cross‐modal correlations. To improve the accuracy of the response spectrum analysis method for building structures, this paper proposes a Deep learning‐based modal Combination (DC) rule by introducing modal contribution coefficients predicted by a deep neural network (DNN) model. The DC rule enhances prediction accuracy by considering the characteristics of ground motion and the dynamic properties of a structural system. The DC rule provides more accurate predictions than the conventional rules, particularly for irregular response spectra and responses affected by higher modes. The efficiency and applicability of the DC rule are demonstrated by numerical investigations of multistory shear buildings and steel frame structures with regular and irregular shapes. The source codes, data, and trained models are available for download at https://github.com/tyongkim/ERD2.

Revisiting complex dynamic systems theory: Empowering language teachers and teaching

AbstractThis article revisits complex dynamic systems theory (CDST) and provides a new synthesis that, the authors argue, may empower language teachers. The particular focus is on the interplay between change and stability in complex dynamic systems, including language teaching and learning. The article identifies four key dynamical properties of complex dynamic systems, which reflect change, stability, and the interplay between these two. The dynamical properties are historicity, adaptiveness, nonlinearity, and emergence. The authors associate these dynamic properties with four recognisable types of activity: normative, contingent, creative, and purposeful teaching and learning. The central argument is that language teaching and learning are interconnected, and language teaching that promotes these four types of teaching and learning activity may also promote opportunities for language learning. The authors conclude with a discussion of how teachers may use this CDST perspective to reflect on three aspects of their professional context—teaching, language, and agency—and how such reflection, followed by action, may promote opportunities for language learning in their contexts.

Hydrological records can be used to reconstruct the resilience of watersheds to climatic extremes

Hydrologic resilience modeling is used in public watershed management to assess watershed ability to supply life-supporting ecoservices under extreme climatic and environmental conditions. Literature surveys criticize resilience models for failing to capture watershed dynamics and undergo adequate testing. Both shortcomings compromise their ability to provide management options reliably protecting water security under real-world conditions. We formulate an empirical protocol to establish real-world correspondence. The protocol applies empirical nonlinear dynamics to reconstruct hydrologic dynamics from watershed records, and analyze the response of reconstructed dynamics to extreme regional climatic conditions. We devise an AI-based early-warning system to forecast (out-of-sample) reconstructed hydrologic resilience dynamics. Application to the La Tejería (Spain) experimental watershed finds it to be a low dimensional nonlinear deterministic dynamic system responding to internal stressors by irregularly oscillating along a watershed attractor. Reconstructed and forecasted hydrologic resilience behavior faithfully captures monthly wet-cold/dry-warm weather patterns characterizing the Mediterranean region.

Generalized time-delay reverse synchronization with error feedback coefficients

To enhance the application of discrete chaotic systems in secure communication, we introduce a novel generalized time-delay inverse synchronization method with error feedback coefficient. This paper outlines the derivation of an inverse master-slave time-delay generalized synchronization system using the Lyapunov theory with error feedback coefficient design, which is proposed for the first time. To verify the efficacy of the synchronization method, we constructed a new 4D discrete hyperchaotic system. The dynamic properties of the novel system, such as the phase diagram and Lyapunov exponents, are investigated. Empirical outcomes reveal that generalized discrete time-delay synchronization can be accomplished under certain conditions for the error feedback coefficient. The study utilizes the chaotic masking technique to encrypt and decrypt messages in the secure communication system. The experimental findings reveal that by integrating the synchronization approach with the time-delay context of secure communication, the applicable design of the synchronization procedure is adaptable and trustworthy, catering to the pertinent requirements of engineering, and has the capacity to attain instantaneous chaotic synchronization requisites.

The connection between the dynamical properties of 3D systems and the image of the energy-Casimir mapping

The connection between the dynamical properties of 3D systems and the image of the energy-Casimir mapping

Dynamic load distribution property of transmission system during rice harvesting process

The average time between failures of Chinese combine harvester was far below the advanced combine harvester in Europe and America. A load test system was designed and built on the transmission structure of combine harvester. The dynamic load of the transmission structure was tested on rice harvesting in the field and used to compare with calculated values of maximum load capacity. The damage mechanism and load distribution of transmission structure would be obtained. The test results showed that the average and peak power consumptions of each working part increased with the increase in the speed of the combine harvester. As the stubble height increased, the average and peak power consumptions of each component correspondingly increased with the increase in the load on the entire machine. The power consumptions of the left and right half shafts of the chassis gradually increased, whereas the power consumptions of the other components did not change significantly. The power consumption of the intermediate shaft ranged from 29.53 to 35.92 kW, and the average power consumption was 34.03 kW when harvesting was done at full load in the field. The limit power consumptions of the left and right half axles of the chassis were 9.35 and 11.55 kW.

ПРОБЛЕМИ ТА ПЕРСПЕКТИВИ РОЗВИТКУ АВТОМАТИЗОВАНИХ СИСТЕМ УПРАВЛІННЯ ЦІЛЕВКАЗАННЯ

The justification of the need to improve the automated control process in the system of automatic targeting testing is presented. The modern Armed Forces of Ukraine use means of automation at all levels of command of the troops and managing the means of defeat. In parallel with the automation of the management process at all levels, the shadows of recent years indicate a shift of attention towards the lower management levels. The command systems at these levels collect, process and analyse information necessary to optimize the management of the actual combat assets. The specific fire task to combat crew, its transfer and delivery to the contractor is an important point in the process of such control. A central part of the task statement is targeting i.e. a brief, clear and understandable message about the location of the target and other information about it. The guaranteed transmission of target instruction from any level of control to the means of destruction is one of the directions of development and improvement of automated control systems for military purposes. The automated method for achieving the target-setting provides a minimum time for setting the firing task and carrying it out. However, in order for it to be revived, information on the full identification of targets at the different levels of control and sufficiently accurate information on the location of its forces and assets is necessary. In many cases, the dynamic properties of such control systems are described by high-order differential equations. The implementation of optimal speed in such cases faces a number of technical difficulties related to the need to calculate and implement the number of intervals of control action.The number of intervals is equal to the order of the differential equation of the system. In this case, it is advisable to move to a quasi-optimal control with the number of controls switching equal to three. Reducing the number of switches will not only simplify the functions of the microprocessor in such a control system, but also increase its reliability. Optimum system theory illuminates the way forward and points to unused reserves of existing automatic control systems. The development of mathematical theory is largely determined by the development of methods of synthesis of optimal systems. Bellman R. and Feldbaum O. first formulated and proved the theorem of n intervals or n switching by control systems. According to the n interval theorem, the number of switches can be reduced by replacing the n-order control system with an equivalent lower-order system. According to the hypothesis of Academician A.Y. Ishlinsky, a third-order system can be found for any n-order system. The paper presents a numerical experiment confirming the hypothesis of Academician A.Y. Ishlinsky about the possibility of presenting a high-order system equivalent to a third-order system. The problem of identifying the dynamics of technological processes is solved by acceleration curves. The use of direct numerical methods is limited in some cases by the inability to implement the input of the required form. In this case, object identification is carried out by a conventional differential equation of order 4. A type of differential equation of order 3 is also known. The values of the parameters at which the solutions of the differential equations of order 4 and order 3 are most closely related are found. To solve the problem, the Nelder-Mead method is used. The solution of the original differential equation is proposed to be found by the Runge-Kutt-Merson method. The obtained results make it possible to simplify the process of object management in the systems of automatic targeting testing. The numerical experiments carried out confirmed the conjecture of Academician A.Y. Ishlinsky that the n-order system can be represented by an equivalent system of order 3. Thus, to reduce the time required to collect, process and analyze information necessary for the management of combat assets.

Invariable distribution of co-evolutionary complex adaptive systems with agent's behavior and local topological configuration.

In this study, we developed a dynamical Multi-Local-Worlds (MLW) complex adaptive system with co-evolution of agent's behavior and local topological configuration to predict whether agents' behavior would converge to a certain invariable distribution and derive the conditions that should be satisfied by the invariable distribution of the optimal strategies in a dynamical system structure. To this end, a Markov process controlled by agent's behavior and local graphic topology configuration was constructed to describe the dynamic case's interaction property. After analysis, the invariable distribution of the system was obtained using the stochastic process method. Then, three kinds of agent's behavior (smart, normal, and irrational) coupled with corresponding behaviors, were introduced as an example to prove that their strategies converge to a certain invariable distribution. The results showed that an agent selected his/her behavior according to the evolution of random complex networks driven by preferential attachment and a volatility mechanism with its payment, which made the complex adaptive system evolve. We conclude that the corresponding invariable distribution was determined by agent's behavior, the system's topology configuration, the agent's behavior noise, and the system population. The invariable distribution with agent's behavior noise tending to zero differed from that with the population tending to infinity. The universal conclusion, corresponding to the properties of both dynamical MLW complex adaptive system and cooperative/non-cooperative game that are much closer to the common property of actual economic and management events that have not been analyzed before, is instrumental in substantiating managers' decision-making in the development of traffic systems, urban models, industrial clusters, technology innovation centers, and other applications.

Contract-Based Design for Hybrid Dynamical Systems and Invariance Properties

This work establishes fundamental principles for verifying contract for interconnected hybrid systems. When system’s hybrid arcs conform to the contract for a certain duration but subsequently violate it, the composition of hybrid dynamical systems becomes challenging. The objective of this work is to analyze the temporal satisfaction of the contract, allowing us to reason about the compositions that do not violate the contract up to a certain point in a hybrid time. Notions of weak and strong satisfaction of an assume-guarantee contract are introduced. These semantics permits the compositional reasoning on hybrid systems of varying complexity depending on the interconnection’s type, feedback or cascade. The results show that both semantics are compatible with cascade composition, while strong semantic is required for feedback composition. Moreover, we have shown how one can go from weak to strong contract satisfaction. Finally, we have studied a particular class of hybrid systems and we have shown that the concept of forward (pre-)invariant relative to a contract makes it possible to deal with feedback compositions. These results are demonstrated throughout the paper with simple numerical examples.