Analysis Of Dynamical Systems Research Articles

Dynamic analysis of TBM multi-gear parallel transmission system considering the influence of multiple factors

Dynamic analysis of TBM multi-gear parallel transmission system considering the influence of multiple factors

Estimation of effective damping ratio for cast-in-place tunnel-form system and evaluation of its role in performance point prediction

The extensive time and computational effort are primary challenges in nonlinear dynamic analysis of tunnel-form concrete systems. These challenges lead engineers to resort to simpler, pushover-based analyses, inherently based on estimating the seismic performance point of the system. Technical literature review indicates that no study has yet rigorously evaluated the accuracy of existing methods for estimating the performance point of tunnel-form systems. To eliminate potential ambiguities, in this study, the seismic performance point of the system under design basis earthquake (with a 475-year return period) has been calculated using three different methods (i.e., displacement coefficient, capacity spectrum, and displacement amplification factor), and compared with the results of accurate nonlinear time-history analysis. In the range of 5-, 7-, and 10-story models studied, the results indicate the inefficiency and insufficiency of the mentioned methods. Investigations reveal that while the capacity spectrum method provides better results, but its process is lengthy, and the displacement coefficient method significantly overestimates the performance point (with more than 80 % error). It was also evident that the displacement amplification factor underestimates the performance point and contradicts the direction of confidence. Based on observations, the use of all three methods for the tunnel-form system requires modifications. The calculated values of effective damping ratio for the tunnel-form system explicitly indicate type A behavior according to the ATC-40 classification. By presenting this parameter in a multi-level format, the shortcomings of both capacity spectrum and displacement coefficient methods are easily addressed. Referring to the results, the calculated value of the displacement amplification factor in the system exceeds the recommended value by the seismic design code, and by adjusting it, satisfactory responses can be obtained in the method based on the displacement amplification factor. Finally, introducing the “probable performance interval” parameter, recommending its use instead of the “performance point” parameter in assessments by pushover analysis is suggested. This parameter is applicable with all three mentioned methods and has been introduced in this study as a desirable factor in compensating for inherent uncertainties related to future earthquakes.

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

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

A mathematical treatment of the impact of p53 signalling on the expression of the transcription factor E2F in the CycE/Cdk2 subsystem in cancerous cells

Complex networks of proteins and genes control cell growth until mitosis. These components play crucial roles in determining the characteristics and timing of each reaction in the cell. A family of cyclins and cyclin-dependent kinases regulates the progression of the cell from one stage to the next, while certain inhibitors regulate cell proliferation, significantly impacting this process. We examine the impact of p53 protein production in the cyclin E/cyclin-dependent kinase 2 (CycE/CDK2) subsystem. Although the precise functioning of the p53 protein is not fully understood, it is known to exhibit pulsatile behaviour, triggered in response to DNA damage. Consequently, the expression of the p53 protein within the cell system increases with the severity of DNA damage. Similarly, levels of CycE/CDK2 are substantially elevated in instances of DNA damage.To investigate this subsystem, we have developed a mathematical model of the CycE/CDK2 subsystem, presented as non-linear ordinary differential equations. Our primary aim is to determine the conditions that could theoretically result in tumorigenesis. We conduct a dynamical systems analysis to investigate the presence of stable limit cycles, which indicate the standard operational states of cells. Our investigation reveals the levels of p53 protein at which the cell can correct defects, undergo apoptosis, or enter quiescence, and where the system exhibits a Hopf-bifurcation (limit cycles). This is the novelty of our study, as previous research has primarily focused on numerical simulations.Using MATLAB simulations, we produced various results in response to different expressions and concentrations of the p53 protein, allowing us to assess its influence on malignant cells. By altering the concentration of protein p53, we ascertain the specific cellular circumstances that facilitate its natural growth, self-correction in the presence of defective activity, and entry into a state of quiescence.This investigation is motivated by the significant role of oscillations in driving, controlling, and managing the cellular oversight machinery. These aspects are incorporated into developing a mathematical model that emulates cellular operations. From this research, we establish that E2F is a critical target to mitigate oncogenic activity, achievable by managing the pulsatile behaviour of the inhibitor p53 or inhibiting its production process within the cell machinery.

A dynamic evaluation of an underground transportation system using image processing and centrality index computation

ABSTRACT The study of transportation networks covers a wide range of topics related to managing services and maintaining structures. In order to represent the topological structure of such a network, we associated a graph to a network. Then some different properties or attributes of the network can be managed as weights to be applied to the graph itself. In addition, different centrality indices can be computed in order to identify nodes or edges that are more important or more exposed to capacity changes (such as, for example, disruptive events). The purpose of this research is to provide a methodology for dynamically evaluating the significance of stations in a transportation network. This is accomplished through two distinct phases of activity. Firstly, we propose a dynamic analysis of the underground transportation system of the city of Milan, Italy. This transportation system is the mobility backbone of the city and counts four lines with 110 links and 107 stations, including 21 junctions (the transfer stations that connect the lines). Two data sets about passenger flows (both entering and leaving stations) are used to calculate the flows on links with a resolution of 1 min. The data sets refer to a week in 2018, without the changes in demand due to the pandemic scenario. Data are processed through an ad hoc written assignment procedure. Secondly, a centrality index is calculated by using passenger flows (entering, exiting, and on-segments) as weights of the underground graph. After maps reporting the outcomes of those calculations are drawn, an image comparison is carried out by using image processing tools and different aggregation intervals, in order to investigate how the importance or exposure of each station changes over time. The findings demonstrate that over time, indices vary by station, with junction stations naturally having the highest values. By increasing the observation interval from 1 min up to 30 min, index changes become progressively smoother, like an application of a low pass filter, suggesting that for certain applications (e.g. those concerning security), aggregating data could lead to misleading conclusions.

Development and Analysis of novel Integrable Nonlinear Dynamical Systems on Quasi-One-Dimensional Lattices. Parametrically Driven Nonlinear System of Pseudo-Excitations on a Two-Leg Ladder Lattice

Following the main principles of developing the evolutionary nonlinear integrable systems on quasi-one-dimensional lattices, we suggest a novel nonlinear integrable system of parametrically driven pseudo-excitations on a regular two-leg ladder lattice. The initial (prototype) form of the system is derivable in the framework of semi-discrete zero-curvature equation with the spectral and evolution operators specified by the properly organized 3 × 3 square matrices. Although the lowest conserved local densities found via the direct recursive method do not prompt us the algebraic structure of system’s Hamiltonian function, but the heuristically substantiated search for the suitable two-stage transformation of prototype field functions to the physically motivated ones has allowed to disclose the physically meaningful nonlinear integrable system with time-dependent longitudinal and transverse inter-site coupling parameters. The time dependencies of inter-site coupling parameters in the transformed system are consistently defined in terms of the accompanying parametric driver formalized by the set of four homogeneous ordinary linear differential equations with the time-dependent coefficients. The physically meaningful parametrically driven nonlinear system permits its concise Hamiltonian formulation with the two pairs of field functions serving as the two pairs of canonically conjugated field amplitudes. The explicit example of oscillatory parametric drive is described in full mathematical details.

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

Analysis of a nonlinear dynamic absorption system

Analysis of a nonlinear dynamic absorption system

A decentralized control approach in hypergraph distributed optimization decomposition cases

We study the main decomposition approaches (primal, dual and primal–dual) for a distributed optimization problem from a dynamical system perspective where the couplings among the variables of the optimization problem are described by an undirected, unweighted hypergraph. We conduct stability analysis for the respective dynamical systems of the decomposition cases by using non linear decentralized control theoretic techniques and spectral properties of the respective communication matrices, i.e., the incidence and the Laplacian matrices of the hypergraph. Finally, we provide numerical simulations under a specific coalitional setting that demonstrate the superiority of the hypergraph compared to its respective graph analogue, the clique expansion graph, for the given decomposition algorithms in terms of convergence rate and information transmission efficiency.

Dynamic Characteristics Analysis of the DI-SO Cylindrical Spur Gear System Based on Meshing Conditions

The dual-input single-output (DI-SO) cylindrical spur gear system possesses advantages such as high load-carrying capacity, precise transmission, and low energy loss. It is increasingly becoming a core component of power transmission systems in maritime vessels, aerospace, marine engineering, and construction machinery. In practical operation, the stability of the DI-SO cylindrical spur gear system is influenced by complex excitations. These excitations lead to nonlinear vibration, meshing instability, and noise, which affect the performance and reliability of the entire equipment. Hence, the dynamic performance of the DI-SO cylindrical spur gear system is thoroughly investigated in this research. The impact of excitations and nonlinear factors on the dynamic characteristics was investigated comprehensively. A comparative analysis of the gear system was conducted by establishing a bending–torsional coupling vibration analysis model under synchronous and asynchronous meshing conditions. Nonlinear factors such as periodic time-varying meshing stiffness, meshing damping, friction coefficient, friction arms, load sharing ratio, comprehensive transmission error, and backlash were considered in the proposed model. Then, the effect laws of excitations and nonlinear factors such as meshing frequency, driving load fluctuation, backlash, and comprehensive transmission error were analyzed. The results indicate that the dynamic characteristics exhibited staged stable and unstable states under different meshing frequencies and meshing conditions. At the medium-frequency meshing stage (0.96 × 104~1.78 × 104 Hz), alternating phenomena of multi-periodic, quasi-periodic, and chaotic motion states were observed. Moreover, the root mean square value (RMS) of the dynamic transmission error (DTE) in the asynchronized gear system was generally higher than that in the synchronized gear system. It was found that selecting the appropriate meshing condition could effectively reduce the amplitude of the DTE. Additionally, the dynamic performance could be significantly improved by adjusting control parameters such as driving load fluctuation (0~179 N), backlash (0.8 × 10−4~0.9 × 10−4 m), and comprehensive transmission error (7.9 × 10−4~9.4 × 10−4 m). The research results provide a theoretical guidance for the design and optimization of the DI-SO cylindrical spur gear system.

A Comprehensive Study On The Business Feasibility, And Optimization Model For Paddy Cultivation On Marginal Agricultural Land In Pekalongan District

Paddy cultivation on marginal land is the agribusiness activity. The aim of this research is to assess the feasibility status of paddy cultivation on marginal land and make efforts to optimize based on dynamic modeling system analysis. The research method used is descriptive quantitative with the dynamic modeling system analysis. The results show that the business profitability analysis shows a profit value of IDR 30,486,500, R/C Ratio 2.30, BEP unit 6,316 kg, BEP Sales IDR 15,477,220,-, and returnability 1.30%. This means this business is very profitable. The results of business financial analysis show an NPV IDR 2,536,754,052,-, profitability index 21.36%, IRR 14.21%, and payback period 14.4 years. This means this business is very worthy for development. The results of the dynamic modeling system analysis show that the paddy growth rate is influenced by using technology. Technology will influence rice growth of 3.5-7.0 cm. Nutrients influence the paddy biomass on marginal land. Using 10-20 kg/Ha of fertilizer will affect paddy biomass growth of 35-70 kg/Ha. The results of the dynamic model analysis show that the maximum paddy harvest production on marginal land is 25-50 kg/Ha/month with fertilizer use of 45-90 kg/Ha/month. This research concludes that the level of paddy cultivation feasibility on critical land is still quite feasible and profitable to develop. model analysis results show that of using agricultural technology and administering appropriate fertilizer doses will greatly determine the level of rice productivity on marginal agricultural land.

Spectral energy transfer on complex networks: a filtering approach

The spectral analysis of dynamical systems is a staple technique for analyzing a vast range of systems. But beyond its analytical utility, it is also the primary lens through which many physical phenomena are defined and interpreted. The turbulent energy cascade in fluid mechanics, a dynamical consequence of the three-dimensional Navier–Stokes equations in which energy “cascades” from large injection scales to smaller dissipation scales, is a well-known example that is precisely defined only in reciprocal space. Related techniques in the context of networked dynamical systems have been employed with great success in deriving reduced order models. But what such techniques gain in analytical tractability, they often lose in interpretability and locality, as the lower degree of freedom system frequently contains information from all nodes of the network. Here, we demonstrate that a network of nonlinear oscillators exhibits spectral energy transfer facilitated by an effective force akin to the Reynolds stress in turbulence, an example of an emergent higher order interaction. Then, introducing a filter-based decomposition motivated by large eddy simulation, we show that such higher order interactions can be localized to individual nodes and study the effects of local topology on such interactions.

Dynamic analysis of a novel hyperchaotic system based on STM32 and application in image encryption

This paper presents a novel 4D hyperchaotic system derived from a modified 3D Lorenz chaotic system. A key aspect of this system is the presence of a single equilibrium point, and its stability is carefully analyzed. The dynamic properties, including the Lyapunov exponent spectrum, bifurcation diagram, and chaotic attractors, are investigated using MATLAB simulations. The results reveal that the system displays hyperchaotic behavior across a wide range of the parameter d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d$$\\end{document}, with its chaotic attractor transitioning through four states: hyperchaotic, chaotic, periodic, and quasi-periodic, showcasing the system's complex dynamics. Experimental validation using STM32 embedded hardware successfully reproduces these four types of chaotic attractors, confirming the theoretical predictions. The proposed hyperchaotic system is then applied to image encryption, introducing a novel encryption method. The hyperchaotic key sequence generated by this system meets 15 tests of the NIST SP800-22 standard, and further experimental validation with STM32 hardware demonstrates the algorithm's effectiveness, simplicity, non-linearity, and high security. The encrypted images and sequences are rigorously tested key space analysis, histogram similarity analysis, information entropy analysis, statistical attack analysis, differential attack analysis, key sensitivity analysis, and correlation analysis, highlighting the robustness and reliability of the proposed system. This method is versatile and can be extended to various fields, including audio and video encryption, text encryption, IoT security, financial transaction security, and medical data protection.

An evaluation method of construction reliability of cable system of cable-stayed bridge based on Bayesian network

PurposeAs an important load-bearing component of cable-stayed bridge, the cable-stayed cable is an important load-bearing link for the bridge superstructure and the load transferred directly to the bridge tower. In order to better manage the risk of the cable system in the construction process, the purpose of this paper is to study a new method of dynamic risk analysis of the cable system of the suspended multi-tower cable-stayed bridge based on the Bayesian network.Design/methodology/approachFirst of all, this paper focuses on the whole process of the construction of the cable system, analyzes the construction characteristics of each process, identifies the safety risk factors in the construction process of the cable system, and determines the causal relationship between the risk factors. Secondly, the prior probability distribution of risk factors is determined by the expert investigation method, and the risk matrix method is used to evaluate the safety risk of cable failure quantitatively. The function expression of risk matrix is established by combining the probability of risk event occurrence and loss level. After that, the topology structure of Bayesian network is established, risk factors and probability parameters are incorporated into the network and then the Bayesian principle is applied to update the posterior probability of risk events according to the new information in the construction process. Finally, the construction reliability evaluation of PAIRA bridge main bridge cable system in Bangladesh is taken as an example to verify the effectiveness and accuracy of the new method.FindingsThe feasibility of using Bayesian network to dynamically assess the safety risk of PAIRA bridge in Bangladesh is verified by the construction reliability evaluation of the main bridge cable system. The research results show that the probability of the accident resulting from the insufficient safety of the cable components of the main bridge of PAIRA bridge is 0.02, which belongs to a very small range. According to the analysis of the risk grade matrix, the risk grade is Ⅱ, which belongs to the acceptable risk range. In addition, according to the reverse reasoning of the Bayesian model, when the serious failure of the cable system is certain to occur, the node with the greatest impact is B3 (cable break) and its probability of occurrence is 82%, that is, cable break is an important reason for the serious failure of the cable system. The factor that has the greatest influence on B3 node is C6 (cable quality), and its probability is 34%, that is, cable quality is not satisfied is the main reason for cable fracture. In the same way, it can be obtained that the D9 (steel wire fracture inside the cable) event of the next level is the biggest incentive of C6 event, its occurrence probability is 32% and E7 (steel strand strength is not up to standard) event is the biggest incentive of D9 event, its occurrence probability is 13%. At the same time, the sensitivity analysis also confirmed that B3, C6, D9 and E7 risk factors were the main causes of risk occurrence.Originality/valueThis paper proposes a Bayesian network-based construction reliability assessment method for cable-stayed bridge cable system. The core purpose of this method is to achieve comprehensive and accurate management and control of the risks in the construction process of the cable system, so as to improve the service life of the cable while strengthening the overall reliability of the structure. Compared with the existing evaluation methods, the proposed method has higher reliability and accuracy. This method can effectively assess the risk of the cable system in the construction process, and is innovative in the field of risk assessment of the cable system of cable-stayed bridge construction, enriching the scientific research achievements in this field, and providing strong support for the construction risk control of the cable system of cable-stayed bridge.

Teleparallel gravity and quintessence: The role of nonminimal boundary couplings

In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for both the torsion scalar (T) and the boundary term (B). We have examined three well-motivated forms of potential functions and constrained the model parameters through dynamical system analysis. This analysis has played a crucial role in identifying cosmologically viable models. We have analysed the behaviour of dynamical parameters such as equation-of-state parameters, as well all the standard density parameters for radiation, matter, and DE to assess their compatibility with current observational data. The phase space diagrams are presented to support the stability conditions of the corresponding critical points. The Universe is apparent in its late-time cosmic acceleration phase via the DE-dominated critical points. Additionally, we compare our findings with the most prevailing ΛCDM model. The outcomes are further inspected using the cosmological data sets of Supernovae Ia and the Hubble rate H(z).

Koopman analysis of the singularly perturbed van der Pol oscillator.

The Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator, the so-called Koopman eigenvalues and Koopman eigenfunctions, respectively, mirror global properties of the system's flow. In this paper, we perform the Koopman analysis of the singularly perturbed van der Pol system. First, we show the spectral signature depending on singular perturbation: how two Koopman principal eigenvalues are ordered and what distinct shapes emerge in their associated Koopman eigenfunctions. Second, we discuss the singular limit of the Koopman operator, which is derived through the concatenation of Koopman operators for the fast and slow subsystems. From the spectral properties of the Koopman operator for the singularly perturbed system and the singular limit, we suggest that the Koopman eigenfunctions inherit geometric properties of the singularly perturbed system. These results are applicable to general planar singularly perturbed systems with stable limit cycles.

Dynamic impact analysis of the time-delay levitation control system on maglev vehicle system after adding smith predictor

The time delay (TD) in the levitation control system significantly affects the dynamic performance of the closed-loop system in electromagnetic suspension (EMS) maglev vehicles. Excessive TD can cause levitation instability, making it essential to explore effective mitigation methods. To address this issue, a Smith Predictor (SP) is integrated into the traditional PID levitation control system. The combination of theoretical analysis and numerical simulation is employed to assess the stability of the time-delay levitation control system after the integration of the Smith Predictor. Theoretical analysis reveals that when TD exceeds a critical threshold, the levitation system becomes unstable. The addition of SP alters the root trajectory of the system characteristic equation from positive to negative, and recovers the levitation system to stable status. Assuming complete knowledge of the dynamic system, the TD compensation value in the SP becomes a key parameter that determines its performance. A minimum effective value (MEV) for TD compensation is identified, correlating with the system's stability region. Under the influence of TD, more complex systems and higher running speeds of the maglev vehicle lead to a narrower stable region and a larger MEV for TD compensation. Given the simulation parameters in this paper, with a system TD of 15 ms and a maximum vehicle speed of 160 km/h, the MEV for TD compensation in the SP should be set at 12 ms.

Sustainable Development of Digital Cultural Heritage: A Hybrid Analysis of Crowdsourcing Projects Using fsQCA and System Dynamics

Cultural heritage crowdsourcing has emerged as a promising approach to address the challenges of digitizing and preserving cultural heritage, contributing to the sustainable development goals of cultural preservation and digital inclusivity. However, the long-term sustainability of these projects faces numerous obstacles. This study explores the key configurational determinants and dynamic evolutionary mechanisms driving the sustainable development of cultural heritage crowdsourcing projects, aiming to enhance their longevity and impact. An innovative integration of fuzzy-set qualitative comparative analysis (fsQCA) and system dynamics (SD) is employed, drawing upon a “resource coordination–stakeholder interaction–value co-creation” analytical framework. Through a multi-case comparison of 18 cultural heritage crowdsourcing projects, we identify necessary conditions for project sustainability, including platform support, data resources, knowledge capital, and digitalization performance. The study reveals multiple sufficient pathways to sustainability through configurational combinations of participant motivation, innovation drive, social capital, and social impact. Our system dynamics analysis demonstrates that crowdsourcing project sustainability exhibits significant nonlinear dynamic characteristics, influenced by the interaction and emergent effects of the resource–participation–performance chain. This research offers both theoretical insights and practical guidance for optimizing crowdsourcing mechanisms and sustainable project operations, contributing to the broader goals of sustainable cultural heritage preservation and digital humanities development. The findings provide a roadmap for policymakers and project managers to design and implement more sustainable and impactful cultural heritage crowdsourcing initiatives, aligning with global sustainability objectives in the digital age.

Balancing Economy and Ecology: A System Dynamics Analysis of Shrimp Aquaculture and Mangrove Forest Policy

Balancing Economy and Ecology: A System Dynamics Analysis of Shrimp Aquaculture and Mangrove Forest Policy

Dynamic analysis of an adiabatic compressed air energy storage system with temperature-regulated in air tanks

In this study, an innovative temperature regulation method is developed to augment the air storage capacity of adiabatic compressed air energy storage. Hot water, produced by recovering waste heat from the discharging process, is injected into these tanks to control the air temperature as needed. The transient-state calculation models have been established for each component, and validation is performed using experimental data obtained from published work. The utilization of proportion integration differentiation control technology enables precise regulation of the air outlet temperature of heat exchangers, achieving a control accuracy of 1K. The operational status of the components has been investigated, and a comparison is made between the performances of the modified and traditional adiabatic compressed air energy storage systems. The comparative analysis results show that the modified system can achieve a notable round trip efficiency of 71.71 %, which is comparable to that of conventional system (71.41 %). The effective air storage density of the modified system is 47.24 kg/m3, which presents a 15.08 % increase compared to traditional system (41.05 kg/m3). The influence of discharge pressure and pressure difference between threshold pressure and discharge pressure is also investigated. It is found that the modified adiabatic compressed air energy storage shows a consistently greater effective air storage density than traditional system, with a minimum increase exceeding 10.52 %.