Analysis Of Dynamical Systems Research Articles

Dynamic Characteristics, Analysis, and Measurement of a Large Optical Mirror Processing System

Dynamic Characteristics, Analysis, and Measurement of a Large Optical Mirror Processing System

A Geometric Numerical Integration with Simple Cell Mapping for Global Analysis of Nonlinear Dynamical Systems

In order to improve the efficiency in computing the global properties of nonlinear systems, some effective methods have been proposed for the global analysis of these systems. However, there are only few investigations focusing on the numerical algorithms of the system response trajectories. This paper presents a higher-efficiency geometric numerical integration method with simple cell mapping for solving the basins of attraction of nonlinear systems. This numerical algorithm is based on the rule of Lie derivative, using it to calculate the trajectories of the nonlinear systems. Then, the global structure is studied by the numerical algorithm associated with a simple cell mapping method. Compared with the traditional Runge–Kutta methods of orders 4 and 5, it is demonstrated that the proposed Lie derivative iterative algorithm has significant advantages in efficiency.

Effect of electromagnetic radiations on the dynamics of a five-chain coupled inertial Hopfield neural network and control of multi-stability with the selection of a desired attractor.

Abstract In this paper, we investigate the effect of electromagnetic radiation on the dynamics of a network consisting of five chain-coupled inertial Hopfield neurons. The study revealed that the neural system designed such a way involves several complex phenomena, namely Hopf bifurcation, chaos, hyperchaos and the coexistence of up to thirty-two attractors in phase space. The complexity specific to our system is due to the higher number of equilibrium points, namely two hundred and forty-three. Under the conditions of safe functioning of our neural system (chaos or hyperchaos), we have been able to observe that electromagnetic radiation has a harmful character for the system, because we found for a range of variation in the intensity of the electromagnetic feedback induction current a coexistence of chaotic and periodic states (epileptic state). We then controlled the multi-stability using a desired attractor selection scheme, with the aim of suppressing the pathological state. All the work carried out in this contribution is done with the help of dynamical system analysis tools such as the bifurcation diagram, the spectrum and the maximum exponent of Lyapunov, phase portraits and basins of attraction. The scheme used is the Runge-Kutta-4. In order to validate the numerical results, we use analog calculation and some results were derived from the Pspice software. These results are in good accordance in amplitude and location on the plane to those of numerical simulations.

Stability and bifurcation analysis of a 2DOF dynamical system with piezoelectric device and feedback control

This study aims to demonstrate the behaviors of a two degree-of-freedom (DOF) dynamical system consisting of attached mass to a nonlinear damped harmonic spring pendulum with a piezoelectric device. Such a system is influenced by a parametric excitation force on the direction of the spring’s elongation and an operating moment at the supported point. A negative-velocity-feedback (NVF) controller is inserted into the main system to reduce the undesired vibrations that affect the system’s efficiency, especially at the resonance state. The equations of motion (EOM) are derived by using Lagrangian equations. Through the use of the multiple-scales-strategy (MSS), approximate solutions (AS) are investigated up to the third order. The accuracy of the AS is verified by comparing them to the obtained numerical solutions (NS) through the fourth-order Runge-Kutta Method (RK-4). The study delves into resonance cases and solvability conditions to provide the modulation equations (ME). Graphical representations showing the time histories of the obtained solutions and frequency responses are presented utilizing Wolfram Mathematica 13.2 in addition to MATLAB software. Additionally, discusses the bifurcation diagrams, Poincaré maps, and Lyapunov exponent spectrums to show the various behavior patterns of the system. To convert vibrating motion into electrical power, a piezoelectric sensor is connected to the dynamical model, which is just one of the energy harvesting (EH) technologies with extensive applications in the commercial, industrial, aerospace, automotive, and medical industries. Moreover, the time histories of the obtained solutions with and without control are analyzed graphically. Finally, resonance curves are used to discuss stability analysis and steady-state solutions.

Research on the aero-hydro coupling characteristics of the floating twin-rotor wind turbine system

The concept of installing two wind turbines on a floating platform, known as a floating twin-rotor wind turbine system, has recently garnered significant interest. This configuration can harness greater wind energy resources, reduce installation and mooring costs by sharing mooring lines, and minimize losses due to wake effects between turbines through yaw control. However, previous research has not sufficiently addressed the dynamic performance analysis of such systems. This study focuses on a high-capacity floating twin-rotor wind turbine system and develops an aero-hydrodynamic coupled analysis method based on the free vortex wake method and potential flow theory, specifically tailored for the twin-rotor configuration. This method facilitates real-time iterative calculations of wind and wave loads acting on the system and suggests optimization strategies for its design. Our findings indicate that the design of high-capacity floating twin-rotor systems can significantly reduce costs. Furthermore, the twin-rotor floating system design enhances wake recovery and achieves optimal comprehensive performance when the rotor spacing ratio (S/D) is 1.2 for the IEA 15 MW turbine. The coupled interactions induce periodic variations in aerodynamic performance, with the amplitude of these variations increasing with turbulence intensity. This research lays a theoretical foundation for advancing the design, platform optimization, and coupled computational analyses of large-capacity, large-scale floating twin-rotor wind turbine systems.

Dynamic Interaction Analysis of a Coupled System of Permanent Maglev Train and Flexible Track Beam

Vehicle–track beam coupling resonance greatly influences the vibration response of the suspended permanent (SPML) system. Therefore, the study established the coupled dynamic model of the SPML train and the track beam using. The model is used to analyze the dynamic response of SPML trains when passing through the long-span flexible track beam at resonance speed. The accuracy of the model was verified by field tests, which simulated and compared the dynamic responses of maglev train and track beam systems at different running speeds. Furthermore, the coupled vibration response of the train and track beam at resonant speed are investigated to gain insight into the mechanism and vibrational properties of the SPML system in a resonant background. It shows that the dominant frequency of the train, suspension frame, and track beam is 6.74[Formula: see text]Hz. They result in resonance in the SPML system at 30[Formula: see text]km/h. Further analysis shows that adjusting the vertical distance between the mass center of the vehicle and the track beam can effectively alleviate the resonance between the vehicle and the track. Additionally, deformation at the ends of the long-span track beams affects the levitation force and gap of the suspension frame, offering valuable guidance for SPML system design.

Winch Traction Dynamics for a Carrier-Based Aircraft Under Trajectory Control on a Small Deck in Complex Sea Conditions

When the winch traction system of a carrier-based aircraft works under complex sea conditions, the rope and the tire forces are greatly changed compared with under simple sea conditions, and it poses a potential threat to the safety and stability of the aircraft’s traction system. The accurate calculation of the rope and tire forces of a carrier-based aircraft’s winch traction under complex sea conditions is an arduous problem. A novel method of dynamic analysis of the aircraft-winch-ship whole system under complex sea conditions is proposed. A multiple-frequency excitation is adopted to describe the complex sea conditions and the influences of pitching amplitude, and the rolling frequency on the traction dynamics of a carrier-based aircraft along the setting trajectory under complex sea conditions are studied. The advantages and disadvantages of a winch traction system with trajectory control and without trajectory control in complex sea conditions are analyzed. For realizing the trajectory control of the aircraft, the vector difference between the center of mass for the carrier-based aircraft and the position on the predetermined Bessel curve is calculated, so as to obtain the azimuth vector in the aircraft coordinate system. This research is innovative in the modeling of the whole system and the trajectory control of a carrier-based aircraft’s winch traction system under the complicated sea condition of the multi-frequency excitation. ADAMS (Automatic Dynamic Analysis of Mechanical System) is used to verify the correctness of the theoretical calculation for the winch traction. The results show that the complex sea environment has a certain influence on the winch traction safety of the aircraft; in the range of 10–15 s for the traction, the rope force amplitude of complex sea conditions under the multi-frequency excitation is 29.5% larger than that of the single-frequency amplitude, while the vertical force amplitude of the tire is 201.1% larger than that of the single-frequency amplitude. This research has important guiding significance for the selection of rope and tire models for a carrier-borne aircraft’s winch traction in complex sea conditions.

Dynamic stability analysis of the aircraft electrical power system in the more electric aircraft concept

This paper presents the modelling and analysis process of the electrical power management system on board an electrified aircraft conforming to the More/All Electric Aircraft concept. The main objective of the study is to assess the stability of the Electric Power Distribution System under different operational conditions, including the aspect of constant power loads. The paper describes the structure of the system, in which the key role is played by a synchronous generator and a three-phase rectifier converting alternating current AC into direct current DC. To solve the problem, modeling methods in the Matlab/Simulink environment were used, which enabled the analysis of the dynamic properties of the system and the assessment of stability under various types of loads. The obtained test results show that the presence of constant power loads can lead to instability in the EPDS system, manifested by voltage and current oscillations exceeding the standards specified in the MIL-STD-704E standard. The paper also provides tools for predicting system stability without the need to conduct full stability tests, which is important for the design of modern aviation power systems. The final section of the work presents the research results obtained and the resulting significant insights and practical conclusions.

Cosmology in modified f (𝒢) gravity: a late-time cosmic phenomena

ABSTRACT In this work, we present a method for numerically solving the Friedmann equations of modified $f(\mathcal {G})$ gravity in the presence of pressureless matter. This method enables us to predict the redshift behaviour of the Hubble expansion rate. To evaluate the credibility of the model, we applied a Bayesian MCMC technique using late-time cosmic observations to impose limitations on the free parameters of the Gauss–Bonnet model. Our results suggest that the $f(\mathcal {G})$ model can reproduce the low-redshift behaviour of the standard Lambda cold dark matter ($\Lambda$CDM) model, but there are significant differences at high redshifts, leading to the absence of a standard matter-dominated epoch. We also examined the profiles of cosmographic parameters using the model parameter values from the standard range to verify the intermediate epochs. Our analysis shows that the highly promising $f(\mathcal {G})$ model is a feasible candidate for explaining the current epochs. We presented a dynamical system analysis framework to examine the stability of the model. Our study identified critical points depicting various phases of the Universe and explained the evolutionary epochs. We demonstrated that the model effectively captures the evolution of energy components over cosmic time, supporting its validity as an alternate explanation for the observed acceleration of the Universe.

Dynamical system analysis in modified Galileon cosmology

Abstract In this paper, we have investigated the phase space analysis in modified Galileon cosmology, where the Galileon term is considered a coupled scalar field, $F(\phi)$. We focus on the exponential type function of $F(\phi)$ and the three well-motivated potential functions $V(\phi)$. We obtain the critical points of the autonomous system, along with their stability conditions and cosmological properties. The critical points of the autonomous system describe different phases of the Universe. The scaling solution for critical points was found in our analysis to determine the matter-dark energy and radiation-dark energy-dominated eras of the Universe. In these scaling solutions, dark energy is typically introduced alongside another component, such as radiation or matter, and helps explain the transition between cosmological eras. The dark energy dominated critical points show stable behavior and indicate the late-time cosmic acceleration phase of the Universe. Further, the results are examined with the Hubble rate $H(z)$ and the Supernovae Ia cosmological data sets.

Dynamical system analysis for scalar field potential in teleparallel gravity

AbstractIn this paper, we have presented a power law cosmological model and its dynamical system analysis in $$f(T,\phi )$$ f ( T , ϕ ) gravity, where T is the torsion scalar and $$\phi $$ ϕ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) , the exponential form and the power law form, with exponential scalar field potential, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter agree with the result of recent cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

Nonlinear dynamic analysis of spindle system considering thermal-solid coupling

Nonlinear dynamic analysis of spindle system considering thermal-solid coupling

Dynamic characteristic analysis of the elastic ring squeeze film damper-rotor system considering coupling angular misalignment

Dynamic characteristic analysis of the elastic ring squeeze film damper-rotor system considering coupling angular misalignment

Coupling dynamic analysis of underwater vehicle-manipulator system based on enhanced disturbance map

Coupling dynamic analysis of underwater vehicle-manipulator system based on enhanced disturbance map

Optimizing prediction accuracy in dynamic systems through neural network integration with Kalman and alpha-beta filters.

In the realm of dynamic system analysis, the Kalman filter and the alpha-beta filter are widely recognized for their tracking and prediction capabilities. However, their performance is often limited by static parameters that cannot adapt to changing conditions. Addressing this limitation, this paper introduces innovative neural network-based prediction models that enhance the adaptability and accuracy of these conventional filters. Our approach involves the integration of neural networks within the filtering algorithms, enabling the dynamic augmentation of parameters in response to performance feedback. We present two modified filters: a neural network-based Kalman filter and an alpha-beta filter, each augmented to incorporate neural network-driven parameter tuning. The alpha-beta filter is enhanced with neural network outputs for its α and β parameters, while the Kalman filter employs a neural network to optimize its internal parameter R and noise factor F. We assess these advanced models using the root mean square error (RMSE) metric, where our neural network-based alpha-beta filter demonstrates a significant 38.2% improvement in prediction accuracy, and the neural network-based Kalman filter achieves a 53.4% enhancement. Hence, our novel approach of integrating neural networks into filtering algorithms stands out as an effective strategy to significantly enhance their performance in dynamic environments.

Bifurcation analysis of Van der Pol–Mathieu equation for the dust grain charge with regularized (κ)-distributed electron-ion

This paper presents a novel viewpoint on nonlinear dust-acoustic waves (DAWs) in an unmagnetized collisionless plasma containing regularized [Formula: see text] distributed electrons and ions (ei) and negative dust grain. The nonlinear oscillatory system based on hybridization of the Van der Pol–Mathieu equation (VdPME) is derived by a new technique. By bifurcation analysis of the planar dynamical system (DS), the effects of parameters with the assistance of phase planes and time series of VdPME are studied. After analyzing the equation to identify the resonance region, a fourth-order Runge–Kutta method is used to solve it numerically. We explained the behavior of DA periodic, stable limit cycle, and chaotic limit cycle wave solutions with different parameters. These types of numerical solutions are illustrated in two-dimensional and three-dimensional graphics by changing the rate at which charged dust grain is produced [Formula: see text], as well as waste [Formula: see text] and comparing the results with those of earlier research. A novel bifurcation analysis of VdPE and VdPME is obtained with the effects of the cut-off factor [Formula: see text] of regularized [Formula: see text]-distribution (RKD) distributed ei, the superthermality of ei particles [Formula: see text], the ratio of ion to electron temperature [Formula: see text], and the ratio of dust to electron density [Formula: see text] illustrated. It is noticed that the DAW shows promotion in width and amplitude as the frequency [Formula: see text] increases and it becomes rarefaction as the cut-off parameter [Formula: see text] increases. On the contrary, it becomes compressive under the impact of superthermality [Formula: see text] and [Formula: see text]. The obtained conclusions may help explain and comprehend a variety of applications in experimental plasma containing highly energy regularized [Formula: see text] dispersed ei, as well as in the interstellar medium.

High-speed nonlinear dynamic analysis of dual springs system considering internal structural impact

The significant dynamic responses of helical springs are widely reported as the main reason causing pre-failure in various high-speed conditions. Though the concept of nonlinear springs is proposed to reduce their own dynamic responses, they are found to induce unexpected spike forces during operations. This study presents a dual springs system used within high-speed sports car engines, which aims to mitigate the dynamic responses and spike forces. Analytical models are first developed to calculate the fundamental frequencies of the outer and the inner springs of the system. Then, a transient finite element (FE) model is developed to accurately simulate the dual springs system working at various high engine speeds and validated experimentally by the results of the engine head tests. The simulations reveal that the use of dual springs with different natural frequencies can mitigate the dynamic responses of the whole system to a certain extent. Nevertheless, it is still a compromise as coil clash occurs on each isolated spring though the effects are reduced. The findings of this study indicate that the establishment of direct connections between every component spring would be a promising way to better mitigate the dynamic responses including the effects of coil clash.

Quantum algorithm for dynamic mode decomposition integrated with a quantum differential equation solver

We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of a dynamic mode decomposition algorithm used in diverse fields such as fluid dynamics, molecular dynamics, and epidemiology. Our quantum algorithm can also compute matrix eigenvalues and eigenvectors by analyzing the corresponding linear dynamical system. Our algorithm handles a broad range of matrices, particularly those with complex eigenvalues. The complexity of our quantum algorithm is O(polylogN) for an N-dimensional system. This is an exponential speedup over known classical algorithms with at least O(N) complexity. Thus, our quantum algorithm is expected to enable high-dimensional dynamical systems analysis and large matrix eigenvalue decomposition, intractable for classical computers. Published by the American Physical Society 2024

Influence of hip prosthesis position on postoperative gait in symptomatic hip osteoarthritis secondary to hip dysplasia patients after primary total hip arthroplasty: a short-term follow-up study

BackgroundThe aim of this study was to analyze the influence of the positioning of the components of total hip arthroplasty (THA) evaluated by the acetabular anteversion (AA) and femoral anteversion (FA) angle on postoperative gait in patients with symptomatic hip osteoarthritis secondary to hip dysplasia undergoing THA.MethodsBetween May 2023 and May 2024, patients with symptomatic hip osteoarthritis secondary to hip dysplasia (Crowe Type I and IV) who underwent THA were enrolled in the study. The AA angle and FA angle were measured by computer tomography (CT). Gait data were determined by using the Dynamic Right Gait & Posture analysis system. The relationship between FA, AA and gait data was analyzed by Pearson correlation test, subgroup Pearson correlation test, multiple linear regression.ResultsA total of 40 patients (45hips) were included in the study. Compared with preoperative, the patient’s postoperative foot progression angle, foot contact angle, plantarflexion velocity, swing foot speed, gait velocity, cadence, stride length were significantly improved. Preoperative FA is significantly different from postoperative FA (P < 0.05), while the difference between preoperative and postoperative AA is not significant. BMI, Crowe Type, AA were related to change of cadence. The less the postoperative AA of patients, and the more the cadence in the postoperative gait of patients.ConclusionOur study showed that THA could improve the gait function of patients with symptomatic hip osteoarthritis secondary to hip dysplasia. Adjusting AA lower could obtain a much more postoperative cadence.

Dynamic modeling and response analysis of misaligned rotor system with squeeze film dampers under maneuver loads

Dynamic modeling and response analysis of misaligned rotor system with squeeze film dampers under maneuver loads