Properties Of Dynamical Systems Research Articles

Dynamic Analysis of a Bolted Joint Rotor-Bearing System with a Blade–Casing Rubbing Fault

Bolted joints are widely used in aeroengine rotor systems to connect multiple components into an integrated structure and provide sufficient stiffness. The mechanical properties of a bolted joint have a significant effect on rotor dynamics. For modern aeroengine designs, the blade-tip clearance is gradually reduced to improve efficiency, which may lead to rubbing damage and affect safe operation. The mechanical properties of a bolted joint change significantly during the blade–casing rubbing process and influence the dynamic properties of the rotor system. Based on the finite element (FE) modeling method, a 15-node bolted joint rotor system model is established in this paper, in which the bolted joint is represented by a 2-node joint element, and the blade–casing rubbing force is considered. The Newmark method is used to solve the motion equations. The dynamic model is validated by comparing the frequency response characteristics for different numbers of blades with the results provided in other published studies. Based on the established model, the effects of the rotational speed, number of blades, and rubbing stiffness on the dynamic responses, normal rubbing forces, and bending stiffness of the bolted joint are evaluated by numerical simulation. The results show that the response amplitude and bending stiffness of the bolted joint change significantly under blade–casing rubbing faults, and the mean value of the vibration response deviates significantly from 0 as the number of blades increases. Meanwhile, the amplitude of the frequency component fVC and the maximum value of the normal rubbing force also increase as the number of blades increases. The main contribution of this paper is the establishment of a new model for a bolted joint rotor system, considering the time-varying bending stiffness of the bolted joint and the blade–casing rub fault, comparing the simulation results to obtain some general results bridging the current research gap. Meanwhile, the numerical results in this paper can provide a cognitive basis for the blade–casing rubbing fault mechanism of a bolted joint rotor system under the influence of speed, number of blades, and rubbing stiffness. The nonlinear dynamic characteristics observed in the present paper can be applied to the blade–casing rubbing fault diagnosis of turbomachines.

Disturbance-Observer-Based LQR Tracking Control for Electro-Optical System

To improve the dynamic property and the disturbance suppression ability of an electro-optical tracking system, this paper presents a disturbance-observer-based LQR tracking control method. The disturbance-observer-based robust controller is composed of three parts: one is the LQR tracking controller, one is the reference model controller and the other is a compensatory controller designed with the output of the disturbance observer. The uncertainty and disturbances are considered in the controller design. By Lyapunov stability theory and linear matrix inequality (LMI) technique, the sufficient conditions for observer gain and controller gain of the tracking reference model of the electro-optical system are given. Simulation and experimental results show that the proposed method in this paper not only improved the disturbance suppression ability of the electro-optical tracking system but also improved the dynamic property of the electro-optical tracking system, such as rise time, settling time and system overshoot. Specially, compared with other methods in this paper, the tracking accuracy and the disturbance suppression ability of the proposed method are about two to three times higher. The method presented in this paper has important reference value in the field of electro-optical system applications. But, with the development of electro-optical system applications, the tracking accuracy and disturbance suppression ability of the proposed method cannot meet the actual requirements of an electro-optical system. The next step of this paper will consider a variety of practical requirements, such as the controller saturation problem and tracking reference target with strong maneuverability, and further optimize the proposed method.

Dynamic and static properties of quantum Hall and harmonic oscillator systems on the non-commutative plane

We study two quantum mechanical systems on the noncommutative plane using a representation independent approach. First, in the context of the Landau problem, we obtain an explicit expression for the gauge transformation that connects the Landau and the symmetric gauge in noncommutative space. This lead us to conclude that the usual form of the symmetric gauge A⃗=−β2Ŷ,β2X̂, in which the constant β is interpreted as the magnetic field, is not true in noncommutative space. We also be able to establish a precise definition of β as a function of the magnetic field, for which the equivalence between the symmetric and Landau gauges is held in noncommutative plane. Using the symmetric gauge, we obtain results for the spectrum of the quantum Hall system, its transverse conductivity in the presence of an electric field, and other static observables. These results amend the literature on quantum Hall effect in the noncommutative plane in which the incorrect form of the symmetric gauge, in noncommutative space, is assumed. We also study the non-equilibrium dynamics of simple observables for this system. On the other hand, we study the dynamics of the harmonic oscillator in non-commutative space and show that, in general, it exhibits quasi-periodic behavior, in striking contrast with its commutative version. The study of dynamics reveals itself as a most powerful tool to characterize and understand the effects of non-commutativity.

Explicit Solutions and Stability Properties of Homogeneous Polynomial Dynamical Systems

In this paper, we provide a system-theoretic treatment of certain continuous-time homogeneous polynomial dynamical systems (HPDS) via tensor algebra. In particular, if a system of homogeneous polynomial differential equations can be represented by an orthogonally decomposable (odeco) tensor, we can construct its explicit solution by exploiting tensor Z-eigenvalues and Z-eigenvectors. We refer to such HPDS as odeco HPDS. By utilizing the form of the explicit solution, we are able to discuss the stability properties of an odeco HPDS. We illustrate that the Z-eigenvalues of the corresponding dynamic tensor can be used to establish necessary and sufficient stability conditions, similar to these from linear systems theory. In addition, we are able to obtain the complete solution to an odeco HPDS with constant control. Finally, we establish results which enable one to determine if a general HPDS can be transformed to or approximated by an odeco HPDS, where the previous results can be applied. We demonstrate our framework with simulated and real-world examples.

Dynamic modeling and performance analysis of metal hydride hydrogen storage system

Metal hydride hydrogen storage has the advantages of high hydrogen storage volume density, high safety, and high hydrogen purity, which can meet the hydrogen storage and supply needs of fuel cells in both mobile and fixed scenarios. It has become one of the most promising hydrogen storage methods. This work studies the dynamic performance of metal hydride hydrogen storage systems under absorption and desorption process by establishing dynamic models and heat exchange models. The dynamic properties of metal hydride hydrogen storage system are analyzed in different reaction process with the experimental test. Results show that when the ambient temperature is within a certain range, low temperatures are conducive to hydrogen absorption, while high temperatures can improve hydrogen release dynamics. Besides, raising the flow rate of hydrogen and reducing the volume fraction of hydrogen storage materials can help to improve the efficiency of hydrogen absorption and desorption reaction.

A fast time domain solver for the equilibrium Dyson equation

We consider the numerical solution of the real-time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph and the Sachdev-Ye-Kitaev model.

Analysis of Novel 4D Rabinovich-Fabrikant Continuous Dynamical System with Coexistence Attractors

In this paper a new Rabinovitch-Fabrikant (R-F) four dimensional (4D) continuous time dynamical system was generated from three dimensional (3D) Rabinovitch-Fabrikant dynamical system using the state augmentation technique by adding new state variables u. The system employs thirteen terms includes five cross-product terms and one irreversible function. The dynamical behaviors of the system were investigated which include equilibrium points, stability analysis, wave form analysis, phase space analysis, multistability, Hopf-bifurcation, the Lyapunov exponent and Lyapunov dimension. The values of Lyapunov exponents are:L1 = 14.025946, L2 = 0.295151, L3 = −2.854401, L4 = −13.736833. and Lyapunov dimension is (3.83474), so the system is unstable and hyperchaotic with coexistence attractors. Chaos was handled in two ways: adaptive control and adaptive synchronization, it was found that the new system is stable and achieved good results.

Verification of Phase Space Inversions Based on The Initial Conditions of the Chaotic Chen System

Theoretically, an eight-term chaos system is presented. The effect of changing the initial conditions values on behavior Chen system was studied. The basic dynamical properties of system are analyzed like time series, attractor, FFT spectrum, and bifurcation. Where the system appears steady state behavior at initial condition xi , yi , zi equal (0, 0, 0) respectively and it convert to quasi-chaotic at xi ,yi ,zi equal (-0.1, 0.5,-0.6). Finally, the system become hyper chaotic at xi ,yi ,zi equal(-0.5, 0.5,-0.6 ) that can used it in many applications like secure communication.

Dynamical properties of quantum many-body systems with long-range interactions

Dynamical properties of quantum many-body systems with long-range interactions

Periodic orbits in chaotic systems simulated at low precision

Non-periodic solutions are an essential property of chaotic dynamical systems. Simulations with deterministic finite-precision numbers, however, always yield orbits that are eventually periodic. With 64-bit double-precision floating-point numbers such periodic orbits are typically negligible due to very long periods. The emerging trend to accelerate simulations with low-precision numbers, such as 16-bit half-precision floats, raises questions on the fidelity of such simulations of chaotic systems. Here, we revisit the 1-variable logistic map and the generalised Bernoulli map with various number formats and precisions: floats, posits and logarithmic fixed-point. Simulations are improved with higher precision but stochastic rounding prevents periodic orbits even at low precision. For larger systems the performance gain from low-precision simulations is often reinvested in higher resolution or complexity, increasing the number of variables. In the Lorenz 1996 system, the period lengths of orbits increase exponentially with the number of variables. Moreover, invariant measures are better approximated with an increased number of variables than with increased precision. Extrapolating to large simulations of natural systems, such as million-variable climate models, periodic orbit lengths are far beyond reach of present-day computers. Such orbits are therefore not expected to be problematic compared to high-precision simulations but the deviation of both from the continuum solution remains unclear.

Effects of chain length on the structure and dynamics of polyvinyl chloride during atomistic molecular dynamics simulations

ABSTRACT Molecular dynamics (MD) simulations have proven to be useful for predicting and interpreting the conformational and dynamic properties of various polymer-solvent systems. The number of repeat units used to represent a polymer chain in an MD study is intended to provide a balance between the computational demands and the reliability of the specific phenomena being studied. To date, this balance has not received sufficient attention. Here, we investigate how the chain length of an atomistic polymer model influences the structure and dynamics of the polymer in different solvents. Seven different polyvinyl chloride (PVC) models, ranging from 5 to 240 –(CH2CHCl)- repeat units, are studied using atomistic MD simulations in two polar organic solvents: tetrahydrofuran (THF) and dimethylformamide (DMF). After benchmarking our MD results against experimental density data, we calculate polymer end-to-end distances, radii of gyration, radial distribution functions, shape descriptors, end-to-end vector correlation functions, dihedral autocorrelation functions, surface areas, surface electrostatic potentials, glass transition temperature and melt viscosities. Our MD simulations demonstrate that most of these properties converge when approximately 100–120 repeat units are used to represent PVC, and this convergence behaviour is observed in different solvents and at different temperatures.

Regularity of the attractor for a fractional Klein‐Gordon‐Schrödinger system with cubic nonlinearities

We study the long time behavior of the solutions for a weakly damped forced nonlinear fractional Klein‐Gordon‐Schrödinger system for a given considered in the whole space . We prove that this system provides an infinite dimensional dynamical system in that possesses a global attractor in the same space and more particularly that this attractor is in fact a compact set of .

Linear cuts in Boolean networks

Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions between Boolean components. They reproduce, in different degrees, the behaviours emerging in more quantitative models. In particular, regulatory conflicts can prevent the standard asynchronous dynamics from reproducing some trajectories that might be expected upon inspection of more detailed models. We introduce and study the class of networks with linear cuts, where linear components—intermediates with a single regulator and a single target—eliminate the aforementioned regulatory conflicts. The interaction graph of a Boolean network admits a linear cut when a linear component occurs in each cycle and in each path from components with multiple targets to components with multiple regulators. Under this structural condition the attractors are in one-to-one correspondence with the minimal trap spaces, and the reachability of attractors can also be easily characterized. Linear cuts provide the base for a new interpretation of the Boolean semantics that captures all behaviours of multi-valued refinements with regulatory thresholds that are uniquely defined for each interaction, and contribute a new approach for the investigation of behaviour of logical models.

The Exponential Attractor for Partially Dissipative Lattice System of Infinite Dimension

With the wide application of fractional differential equations, the study of dynamic systems of fractional differential equations has become one of the hotspots in the past decade. The attractor theory is one of the research directions of infinite dimensional lattice dynamical system. In paper, Eden et al. Systematically introduced the exponential attractor of deterministic autonomous dynamical system, which is a compact positive invariant set with finite fractal dimension and attracting orbits at exponential rate. The exponential attractor has a finite fractal dimension. Because of the exponential attractiveness, the exponential attractor is more stable under perturbation than the global attractor. Fitzhugh Nagumo equation is a nonlinear partial equation that describes the periodic oscillation of neuronal action potential under constant current stimulation above the threshold. For Fitzhugh Nagumo system, there are many reports on attractors, but few reports on exponential attractors. In this paper, the infinite dimensional lattice Fitzhugh Nagumo system [4] is studied. The specific contents are as follows: In part 1, the background, development and research status of FitzHugh Nagumo lattice system and the main work of this paper are introduced. In part 2, the basic concepts, inequalities and lemmas required in the research of FitzHugh Nagumo lattice system are introduced. In part 3, the initial value problem of FitzHugh Nagumo lattice system is studied. For any initial value ϕ(0), there exists a unique solution ϕ(t) of system (9) and family of mapping S(t) can generate continuous operator semigroup {S(t)} t≥0 on ,. Through lemma 3.2,3.3,3.4, it can be proved that the continuous operator semigroup {S(t)} t≥0 satisfies uniform continuity and is asymptotically compact, thus proving the existence of the exponential attractor of the system.

STATIC AND DYNAMIC PROPERTIES OF THE KAZAKHSTANI PARTY SYSTEM

The purpose of the present article is to analyze the electoral returns of the Kazakhstani elections held in the 1995-2021 period to estimate both the static (such as frag-mentation) and the dynamic properties (fluidity) of the Kazakhstani party system. In addition to estimating the fragmentation and the instability of the party system resulting from parlia-mentary elections, the paper explores the relationship between the static properties of a party system, such as the level of party system fragmentation, and its dynamic properties, such as the level of fluidity of the party system. By doing so, the article reveals that the decrease in the level of fragmentation, measured on the basis of Rae’s index of fractionalization and Laakso and Taagepera’s Effective Number of Parties, was responsible for the growing insta-bility (fluidity) of the Kazakhstani party system.

Application of Remote Sensing to Study Tropical Cyclones/ Hurricane Energetic to Develop Tropical Cyclone/Hurricane Forecasting Models (TCFM/HFM) Through Morphological and Dynamical Properties of Meso-Scale Convective Systems

The present Tropical Cyclones/Hurricane Weather Research and Forecast (TCFM/HWRF) system is capable to forecast the inner core structure of the Tropical Cyclones/Hurricanes out to 5 days. Hence, efforts are to be made to test, evaluate, and improve predictions of Hurricane’s track(motion), intensity, speed, and inner core Structure, beyond 5 days ,through the study of Hurricane energetic in correlation with dynamical fluid motions and physical features (e.g. radiative transfer, chemistry, cloud processes), of meso-scale NH-SH Convective systems in order to develop a unique Tropical Cyclone/Hurricane Forecast Models (TCFM/HFM), acting as an Operational real-time forecast guidance for all global tropical cyclones/hurricanes across the Atlantic, Asia Pacific, North Indian Ocean and Southern Hemisphere ocean basins.

Total stability of equilibria motivates integral action in discrete-time nonlinear systems

Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. Inspired by the continuous-time literature, in this article we investigate the total stability properties of dynamical discrete-time nonlinear systems. Such a property locally relates phase plots of dynamical systems of the same dimension which are “similar enough”. As a consequence, it enables the analysis of robustness properties via simple model difference in the discrete-time context. First, we study how existence of equilibria for a nominal model transfers to sufficiently similar ones. Then, we provide results on the propagation of stability guarantees to perturbed systems. Finally, we relate such properties to the constant output regulation problem by motivating the use of discrete-time integral action in discrete-time nonlinear systems for model robustness purposes.

Dependency of the positive and negative long-time behaviors of flows on surfaces

Long-time behavior is one of the most fundamental properties in dynamical systems. The limit behaviors of flows on surfaces are captured by the Poincaré-Bendixson theorem using the ω-limit sets. This paper demonstrates that the positive and negative long-time behaviors are not independent. In fact, we show the dependence between the ω-limit sets and the α-limit sets of points of flows on surfaces, which partially generalizes the Poincaré-Bendixson theorem. Applying the dependency result to solve what kinds of the ω-limit sets appear in the area-preserving (or, more generally, non-wandering) flows on compact surfaces, we show that the ω-limit set of any non-closed orbit of such a flow on a compact surface is either a subset of singular points or a locally dense Q-set. Moreover, we show the wildness of surgeries to add totally disconnected singular points and the tameness of those to add finitely many singular points for flows on surfaces.

Dynamic adaptive workload offloading strategy in mobile edge computing networks

With the increasing popularity of mobile devices and explosive growth of task processing requirements, edge computing attracts more attention from researchers nowadays since it can improve the QoS and utilize resources of the cloudlets, including mobile devices and base stations, as much as possible. In a Mobile Edge Computing (MEC) network, the workload offloading problem is quite important since it directly influences the latency of the task processing, and many efficient algorithms have been proposed to deal with it. However, most of the existing algorithms only consider the static or quasi-static scenario, and are not suitable for a system with several fast-moving devices. Since that more and more mobile devices with high speed are involved in a MEC system, a new workload offloading strategy is required to adapt to such a dynamic scenario. In this paper, we sufficient consider the dynamic properties of a MEC system, and proposed a dynamic adaptive workload offloading algorithm based on Lyapunov theories and an FC-LSTM based schedule determining algorithm to balance the workload of different cloudlets and minimize the weighted average energy and time consumption of mobile devices. Theoretical analysis and extensive experimental results show that all the proposed algorithms achieve high performance in terms of energy consumption, convergence and latency.

Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System

In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of this new system are studied by means of tools such as bifurcation diagrams, Lyapunov exponents and phase diagrams. The Hopf bifurcation and periodic solutions of this hyperchaotic system are solved analytically. In addition, a new hyperchaotic control strategy is applied, and a comparative analysis of the controlled system is performed.