Analysis Of Dynamical Systems Research Articles

Dynamic response and stability analysis of vehicle systems with double time-delay feedback control

In this paper, the vehicle suspension dynamic response of time delay feedback control is analyzed considering the suspension of the seat. An active suspension vibration reduction control method based on double time-delay feedback control is proposed to further improve the ride comfort. Firstly, the double time-delay dynamic response equation of the system with three degrees of freedom is established. Then, the root mean square values of seat acceleration and body acceleration are used as the objective functions. Meanwhile, the RMS values of suspension dynamic deflection and tire dynamic displacement are used as constraints, and the optimal feedback parameters are obtained using particle swarm optimisation. The Routh-Hurwitz criterion and frequency domain scanning methods are used to verify the stability of the double time-delay system. Finally, simulation in the time domain and frequency domain is accomplished. It is verified that this feedback control method has strong robustness and anti-interference ability.

Extension of dual equivalent linearization to analysis of deterministic dynamic systems: Part 2—multi-parameter equivalent linearization

Extension of dual equivalent linearization to analysis of deterministic dynamic systems: Part 2—multi-parameter equivalent linearization

Dynamic analysis of an infected predator-prey system with prey herd behavior

ABSTRACT To protect themselves from predation, sometimes prey starts roaming in groups and shows herd behavior. This paper addresses the predator-prey system dynamics with prey herd behavior and infection in predators. We explore the conditions under which all equilibria exist and the stability of each equilibrium point of the system. The outcomes of this work suggest that prey herd behavior is beneficial for the prey population when the predators are diseased. Under suitable conditions, the three populations can coexist and maintain the ecological balance of nature.

Observational constrained Weyl type [formula omitted] gravity cosmological model and the dynamical system analysis

Using the cosmological date sets, the cosmological parameters are constrained in this paper, with well known phantom behavioural Hubble parameter. To understand the dynamics of the Weyl type f(Q,T) gravity, functional form of f(Q,T) has been introduced, where Q and T respectively represents the nonmetricity scalar that depends on the Weyl vector (Q=−6w2) and trace of energy–momentum tensor. Using the constrained values of the parameters, the other geometrical parameters are analysed and the accelerating behaviour has been shown. The dynamical parameters and energy conditions are also analysed. Further to get the complete evolutionary behaviour of the Universe, the dynamical system analysis has been performed.

Investigation of the dynamic characteristics of the pneumatic-mechanical drive of the installation movements of machine mechanisms

The creation of new and improvement of existing machines and mechanisms requires the development of drive engineering and the creation of new drive systems capable of competing with currently known circuit solutions. Under these conditions, the creation of combined pneumatic-mechanical drives is an important scientific and technical task. The purpose of this work is to increase the speed at a given accuracy of auxiliary movements of the target mechanisms of technological machines by creating a pneumatic-mechanical drive with improved energy and dynamic characteristics. The technical solution of a positioning pneumatic-mechanical drive of executive movements of technological equipment is presented, mathematical and computer models are developed. In this case, the method of solving the differential equation in the SimInTech program is used. As a result, an oscillogram of transients is obtained. The developed models allow for dynamic analysis of pneumatic-mechanical systems.

Dynamical system analysis of quintessence dark energy model

Our work deals with the dynamical system analysis of quintessence dark energy scalar field model with exponential potential. A dynamical system analysis has been applied at the background level. Using suitable transformation of variables, the evolution equations are reduced to an autonomous system for exponential form of the scalar potential. The critical points are analyzed with center manifold theory and stability has been discussed by using Schwarzian derivative. Finally, cosmological implications of the critical points are discussed and it is found that the stability of the late-time attractor changes for quintessence dark energy model.

Dynamic performance analysis of a new low-temperature nuclear heating system with APROS

ABSTRACT Pool-type low-temperature heating reactor (PLTHR) has attracted considerable attention throughout the world due to its low operating parameters and satisfactory inherent safety in district heating. Exploring the dynamic performance of PLTHR is a prerequisite for designing control systems and developing operation strategies. Until now, the dynamic performance of the district heating system using a 400 MW pool-type low-temperature heating reactor (DHR-400) has not been fully discussed. Based on APROS software, a precise dynamic model for DHR-400 is constructed in this paper. The dynamic responses of DHR-400 under five external variables such as control rod reactivity, first loop flow rate, second loop flow rate, third loop flow rate, and return temperature at the third loop are investigated. The results revealed that the core power variation is not linear with the flow rate variation at the three loops. Core power variations are −16.27, −14.04, and −20.96 MW with a 30% reduction in flow rate at the first loop, the second loop, and the third loop, respectively. Considering safe operation, when there are minor fluctuations in the heating demand, the core power regulation method by adjusting the third loop’s flow rate should be given priority without altering the position of the control rods.

Dynamic analysis of spindle-bearing system considering bearing wear evolution

Dynamic analysis of spindle-bearing system considering bearing wear evolution

On fractional discrete financial system: Bifurcation, chaos, and control

Abstract The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets. This paper introduces a new three-dimensional (3D) fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders. As such, we evaluate when the equilibrium points are stable or unstable at various fractional orders. We use many numerical methods, phase plots in 2D and 3D projections, bifurcation diagrams and the maximum Lyapunov exponent. These techniques reveal that financial maps exhibit chaotic attractor behavior. This study is grounded on the Caputo-like discrete operator, which is specifically influenced by the variance of the commensurate and incommensurate orders. Furthermore, we confirm the presence and measure the complexity of chaos in financial maps by the 0–1 test and the approximate entropy algorithm. Additionally, we offer nonlinear-type controllers to stabilize the fractional financial map. The numerical results of this study are obtained using MATLAB.

Photonic next-generation reservoir computer based on distributed feedback in optical fiber.

Reservoir computing (RC) is a machine learning paradigm that excels at dynamical systems analysis. Photonic RCs, which perform implicit computation through optical interactions, have attracted increasing attention due to their potential for low latency predictions. However, most existing photonic RCs rely on a nonlinear physical cavity to implement system memory, limiting control over the memory structure and requiring long warm-up times to eliminate transients. In this work, we resolve these issues by demonstrating a photonic next-generation reservoir computer (NG-RC) using a fiber optic platform. Our photonic NG-RC eliminates the need for a cavity by generating feature vectors directly from nonlinear combinations of the input data with varying delays. Our approach uses Rayleigh backscattering to produce output feature vectors by an unconventional nonlinearity resulting from coherent, interferometric mixing followed by a quadratic readout. Performing linear optimization on these feature vectors, our photonic NG-RC demonstrates state-of-the-art performance for the observer (cross-prediction) task applied to the Rössler, Lorenz, and Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations, we show that it is possible to scale to high-dimensional systems while maintaining low latency and low power consumption.

A Survey on Energy Methods for Vibroacoustic Analysis of Random Dynamic Systems and Applications

Abstract Engineering can be considered a field of applied physics, as for the design of dynamic systems several aspects such as the strength, parameters of motion, among others, must be estimated for dimensioning, specifications of construction procedures, and operation. In the search for an appropriate model to estimate the dynamic response of a system to a prescribed input, several energy-based methods have been explored over the last decades to address three main issues. Firstly, it is quite rare that a solution for a purely analytical model exists, particularly for complex built-up structures. Secondly, numerical approaches to solve such complex equations of motion of a structure are computationally expensive. Lastly, even if a numerical or analytical solution can be found, there is no warranty that such estimation would be true for an ensemble of nominally identical built-up systems due to uncertainties that are not usually considered by the models. The aim of this work is to present a survey of existing approaches based on equations of energy rather than motion to simplify the computational process and include the effects of uncertainties in the dynamic response, and improvements to such models in regard of other engineering aspects. Additionally, several engineering applications are presented.

Stability analysis of discrete dynamical system using khan-iteration technique

Stability analysis of discrete dynamical system using khan-iteration technique

Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis

Operator learning frameworks have recently emerged as an effective scientific machine learning tool for learning complex nonlinear operators of differential equations. Since neural operators learn an infinite-dimensional functional mapping, it is useful in applications requiring rapid prediction of solutions for a wide range of input functions. A task of a similar nature arises in many applications of uncertainty quantification, including reliability estimation and design under uncertainty, each of which demands thousands of samples subjected to a wide range of possible input conditions, an aspect to which neural operators are specialized. Although the neural operators are capable of learning complex nonlinear solution operators, they require an extensive amount of data for successful training. Unlike the applications in computer vision, the computational complexity of the numerical simulations and the cost of physical experiments contributing to the synthetic and real training data compromise the performance of the trained neural operator model, thereby directly impacting the accuracy of uncertainty quantification results. We aim to alleviate the data bottleneck by using multi-fidelity learning in neural operators, where a neural operator is trained by using a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. We propose the multi-fidelity wavelet neural operator, capable of learning solution operators from a multi-fidelity dataset, for efficient and effective data-driven reliability analysis of dynamical systems. We illustrate the performance of the proposed framework on bi-fidelity data simulated on coarse and refined grids for spatial and spatiotemporal systems.

Flexible multitask computation in recurrent networks utilizes shared dynamical motifs

Flexible computation is a hallmark of intelligent behavior. However, little is known about how neural networks contextually reconfigure for different computations. In the present work, we identified an algorithmic neural substrate for modular computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses revealed learned computational strategies mirroring the modular subtask structure of the training task set. Dynamical motifs, which are recurring patterns of neural activity that implement specific computations through dynamics, such as attractors, decision boundaries and rotations, were reused across tasks. For example, tasks requiring memory of a continuous circular variable repurposed the same ring attractor. We showed that dynamical motifs were implemented by clusters of units when the unit activation function was restricted to be positive. Cluster lesions caused modular performance deficits. Motifs were reconfigured for fast transfer learning after an initial phase of learning. This work establishes dynamical motifs as a fundamental unit of compositional computation, intermediate between neuron and network. As whole-brain studies simultaneously record activity from multiple specialized systems, the dynamical motif framework will guide questions about specialization and generalization.

A dynamical system analysis of bouncing cosmology with spatial curvature

A dynamical system analysis of bouncing cosmology with spatial curvature

KCC theory for a type of nonlinear damped SD oscillators

Smooth and discontinuous (SD) oscillators are the nonlinear models that will exhibit SD dynamics due to continuous variation of the smooth parameter. Kosambi–Cartan–Chern (KCC) theory is a differential geometric theory that describes the deviations from the entire trajectory of the variational equation to the nearby trajectory. This paper presents a completely new dynamical analysis of a type of SD oscillators with nonlinear damping based on the KCC theory. First, the paper gives five KCC geometrical invariants of SD oscillators in the smooth and non-smooth cases, respectively. The results show that the geometric quantities in the non-smooth case cannot be derived directly from the geometric quantities in the smooth case. Second, from these geometric quantities, KCC stability of SD oscillators trajectory at any point except [Formula: see text] is analyzed. Lastly, numerical results show that in some regions that deviate from the equilibrium point of system, the system will exhibit complex and variable dynamical behavior due to small changes in parameters. This paper shows that the KCC theory is also a useful tool in the dynamical analysis of non-smooth systems.

Revisiting the evolution of bow-tie architecture in signaling networks

Bow-tie architecture is a layered network structure that has a narrow middle layer with multiple inputs and outputs. Such structures are widely seen in the molecular networks in cells, suggesting that a universal evolutionary mechanism underlies the emergence of bow-tie architecture. The previous theoretical studies have implemented evolutionary simulations of the feedforward network to satisfy a given input-output goal and proposed that the bow-tie architecture emerges when the ideal input-output relation is given as a rank-deficient matrix with mutations in network link intensities in a multiplicative manner. Here, we report that the bow-tie network inevitably appears when the link intensities representing molecular interactions are small at the initial condition of the evolutionary simulation, regardless of the rank of the goal matrix. Our dynamical system analysis clarifies the mechanisms underlying the emergence of the bow-tie structure. Further, we demonstrate that the increase in the input-output matrix reduces the width of the middle layer, resulting in the emergence of bow-tie architecture, even when evolution starts from large link intensities. Our data suggest that bow-tie architecture emerges as a side effect of evolution rather than as a result of evolutionary adaptation.

Multiphase flow and geomechanical behavior induced by gas production from silty-clay hydrate reservoirs through different horizontal well scenarios

Accurately predicting the coupled response behaviors during production is essential for the exploitation of gas hydrate. However, the multiphase flow and geomechanical analysis for gas production through horizontal wells in fine-grained sediments are few reported. In this study, a coupled thermal–hydraulic-mechanical (THM) model is carried out to assess the production response behaviors under different schemes. The simulation results indicate that the cumulative gas production for dual horizontal wells by depressurization assisted with hot water injection (Winj) is about 4.0 times and 2.46 times as much as that of single horizontal one and dual horizontal wells without Winj during the short-term production, respectively. However, the corresponding multiples in gas production become 2.63 and 1.40 times for the long-term production. The seafloor uplift for these three production scenarios is similar and approximately 0.06 m within 30 days. However, the ultimate seabed subsidence are 1.15 m, 1.56 m and 2.59 m, respectively. The Z-displacement undergoes approximately linear reduction with depth, while the X-displacement exhibits a gradient distribution except in the near-wellbore area. By contrast, dual horizontal wells under the hybrid production condition have the highest gas productivity and the minimal instability risk. Furthermore, the modified Fetkovich formula can effectively perform the inflow dynamic analysis of horizontal well systems by depressurization. These findings provide a reference for determining production strategies involving horizontal wells in silty clay reservoirs.

Electrifying thermal loads vs. installing batteries: A case study on fast frequency resource potentials of the Victorian power system

Literature suggests different technologies and control algorithms to counteract the decrease in system damping and inertia caused by the increasing penetration of inverter-interfaced resources in renewable power systems. Published studies generally focus on comparing different control mechanisms for a single technology and examine a limited number of operating conditions. Technology comparisons are typically limited to small test cases, base on assumptions that no longer hold in renewable-rich systems or are solely based on literature reviews. This work thoroughly compares fast-frequency reserve provision from inverter-based active thermal loads (ATLs) against battery storage. As such, we employ a large-scale multi-level test case representing the future Victorian power system and link steady-state and dynamic analysis. We examine the frequency and voltage performance following distinct disturbances for five days with hourly resolutions. The results suggest that the potential for electrifying residential heating demand in Victoria is enormous and can significantly enhance frequency metrics. Generally, the improvements achieved with the aggregation of ATLs are similar or even higher than employing a large battery.

Critical expert analysis of permanent magnet synchronous motors identification methods and state variable observers

Relevance. In recent years, the oil industry has seen a tendency to transfer low-yield oil wells to intermittent mode. Unregulated electric drive and the open-loop controlled electric drive of electric centrifugal pumping with permanent magnet synchronous motors are typically not suitable for tasks of intermittent operation of wells. Due to objective reasons, there may not be smooth starts and required quality indicators of transient processes, which leads to even more reduction in oil production. The synthesis of a closed-loop electric drive control system of submersible installations is possible only using algorithms for indirect estimation of non-measured mechanical coordinates of the electric drive – state variables identification methods, observers of the rotor angular velocity and the load torque. The installation of sensors of angular velocity and torque on the shaft of the submersible electric motor is associated with technical difficulties, therefore, there is no need for significant modernization of the hardware solutions of the existing electrical equipment system. To date, the theory of identifying non-linear dynamic systems is widely used to derive an indirect estimate of the non-measured state variables of the permanent magnet synchronous motors. The large number of methods presented in scientific sources requires comparative analysis regarding their benefits and disadvantages in order to select the best identification method that meets the requirements of the oil production and takes into account its specificity and features. In this case, identification systems that are focused on minimizing computing power or operating in real time are given priority. Aim. To determine the best in terms of computational complexity and the convenience of practical use method of identifying state variables of permanent magnet synchronous motors operating in submersible oil well pumping units based on comparative analysis of existing methods presented in Russian and foreign sources. Methods. Methods for system analysis and identification of dynamic systems, a method of critical expert analysis. Result and conclusions. The most common methods for identifying and observing the state variables of synchronous motors with permanent magnets have been described in detail, given the general performance of each group of methods, their benefits and disadvantages were reviewed. By comparative critical expert analysis, it was found that for tasks of submersible electric centrifugal pump units electric drive a Luenberger observer, characterized by relatively low computational complexity and ease of setup in engineering practice can be recommended.