Dynamic Behavior Of System Research Articles

Permanence and extinction of the delay tumor-immune system with the stochastic environment

In this paper, we consider dynamical behaviors of the delay tumor-immune system perturbed by the environmental noise. For the stochastic delay tumor-immune system, we prove the existence and uniqueness of the globally positive solution and the boundedness of the solution. Using the stochastic Lyapunov analysis, comparison theorem and strong ergodic theorem, we establish sufficient conditions for the extinction, permanence and existence of the stationary distribution by considering the dynamics on the boundary. Moreover, we study the dynamical behaviors of the solution to the stochastic delay system around the equilibria of the deterministic model. In addition, numerical simulations and discussions are given to illustrate our analysis results. The numerical simulations show that for any delay [Formula: see text], [Formula: see text] is the threshold, which can characterize the stochastic permanence ([Formula: see text]) and extinction ([Formula: see text]) for the stochastic tumor-immune system.

Research on rigid-flexible coupling nonlinear dynamics of light commercial vehicle considering frame flexibility

Commercial vehicles play a vital role in the transportation industry. Generally, there will present a complex nonlinear dynamic behavior composed of periodic, quasi-periodic, and even chaotic vibration in vehicle vertical system under the continuous speed bump excitation. To explore the nonlinear dynamic behavior of vehicle system, a new rigid-flexible coupling nonlinear dynamic model for light commercial vehicle has been developed theoretically with considering the frame flexibility, suspension stiffness and damping nonlinearity, and rubber bushing nonlinearity. The dynamic model for frame and suspension have been developed with discrete element method and lumped mass method, respectively. Then, the flexible frame model has been verified through the mode shape and frequency calculated by finite element simulation. And the rigid-flexible coupling nonlinear dynamic model of a light commercial vehicle has been verified with Adams simulation and testing results. Furthermore, the influence of vehicle speed and the height of speed bump, suspension stiffness and damping, as well as cargo weight and distribution on vehicle system dynamics is analyzed with bifurcation diagram, time history, frequency, phase diagram and Poincare section. The results show the significant and complex effects on the nonlinear vibration of vehicle system, especially the nonlinear damping and the flexible frame.

On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system

This research work focuses on investigating the propagation of ultrasonic waves, which propagate mechanical vibrations of molecules or particles inside materials. Ultrasound imaging is extensively used and deeply rooted in the medical field. The key technologies that form the basis for many different uses in the area include transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, techniques for measuring blood flow and tissue motion, and three-dimensional imaging. The third-order non-linear β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. The exact solutions of different types, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted. These solutions are obtained by using two newly introduced techniques, namely modified generalized Riccati equation mapping method and modified generalized exponential rational function method. Moreover, breather, lump and other waves are extracted by the assistance of logarithmic transformation and different test functions. The used methodologies are extremely effective and possess substantial computing capacity to effectively address the different solutions with a high level of accuracy in these systems. The techniques used are well-known for being effective, simple, and flexible enough to integrate multiple soliton systems into a unified framework. In addition, we provide 2D and 3D graphs that explain the behavior of the solution at various parameter values, under the influence of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-fractional derivatives. The results offered in this study may improve the comprehension of the nonlinear dynamic behavior of the specific system and confirm the efficacy of the approaches used. We expect that our approaches will be beneficial for a wide range of nonlinear models and other problems in the related fields.

Spatiotemporal implicit neural representation as a generalized traffic data learner

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific dimensions or source-dependent patterns, restricting them from unifying representations. Here, we present a novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation. To discern the underlying dynamics in low-dimensional regimes, coordinate-based neural networks that can encode high-frequency structures are employed to directly map coordinates to traffic variables. To unravel the entangled spatial–temporal interactions, the variability is decomposed into separate processes. We further enable modeling in irregular spaces such as sensor graphs using spectral embedding. Through continuous representations, our approach enables the modeling of a variety of STTD with a unified input, thereby serving as a generalized learner of the underlying traffic dynamics. It is also shown that it can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns. We validate its effectiveness through extensive experiments in real-world scenarios, showcasing applications from corridor to network scales. Empirical results not only indicate that our model has significant superiority over conventional low-rank models, but also highlight that the versatility of the approach extends to different data domains, output resolutions, and network topologies. Comprehensive model analyses provide further insight into the inductive bias of STTD. We anticipate that this pioneering modeling perspective could lay the foundation for universal representation of STTD in various real-world tasks. PyTorch implementations of this project is publicly available at:https://github.com/tongnie/traffic_dynamics.

Superposition of standing waves induced ultra high-resolution atom localization

Abstract In this study, we have theoretically demonstrated ultra-high resolution two-dimensional atom localization within a three-level $\lambda$-type atomic medium via superposition of asymmetric and symmetric standing wave fields. Our analysis provides understanding into the precise spatial localization of atomic positions at the atomic level, utilizing advanced theoretical approaches and principles of quantum mechanics. The dynamical behavior of a three-level atomic system is thoroughly analyzed using the density matrix formalism within the realm of quantum mechanics. A theoretical approach is constructed to describe the interaction between the system and external fields, specifically a control field and a probe field. The absorption spectrum of the probe field is thoroughly examined to clarify the spatial
localization of the atom within the proposed configuration. We have theoretically investigated that symmetric and asymmetric superposition phenomena significantly influence the localized peaks within a two-dimensional spatial domain. Specifically, the emergence of one and two sharp localized peaks has been observed within a region of one wavelength domain. We observed notable influences of the intensity of the control field, probe field detuning, and decay rates on atom localization. Ultimately, we have achieved an unprecedented level of ultra-high resolution and precision in localizing an atom within an area smaller than λ/35×λ/35. These findings hold promise for potential applications in domains such as Bose-Einstein condensation, nanolithography, laser cooling, trapping of neutral atoms, and the measurement of center-of-mass wave-functions.

Exploring the dynamics of HIV and CD4+ T-cells with non-integer derivatives involving nonsingular and nonlocal kernel

It is important to examine and comprehend how HIV interacts with the immune system in order to manage the infection, enhance patient outcomes, advance medical research, and support global health and socioeconomic stability. In this study, we formulate the dynamics of HIV infection to investigate the intricate interactions between HIV and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{CD}}4^{ + }$$\\end{document} T-cells. The Atangana-Baleanu and Caputo-Fabrizio derivative frameworks are applied to comprehensively examine the phenomenon of HIV viral transmission. The basic concepts and results of fractional calculus are presented for the analysis of the model. In our work, we focus on the dynamical behavior of HIV and immune system. We introduce numerical schemes to elucidate the solution pathways of the recommended system of HIV. We have shown the influence of various input factors on the solution pathways of the recommended fractional system and highlighted the oscillatory behavior and chaotic nature of the dynamics. Our findings demonstrate the complexity of the system under study by revealing the existence of the chaotic and oscillatory nature in the dynamics of HIV. In order to quantitatively characterize HIV dynamics, a number of simulations are carried out, providing a visual representation of the effects of different input variables. It has been observed that the chaos and the oscillatory behaviour is strongly related to the nonlinearity of the system. The present study provides a basis for further initiatives that try to enhance interventions and policies to lessen the worldwide burden of infection.

Synergistic effects of waste coral powder and metakaolin in cement pastes: Hydration, pore structure, rheology, and strength

Coral reefs are abundant in waste coral powder, and how to utilize coral powder efficiently to construct far-sea projects has become a major focus of research and engineering field, which is conducive to the development of green economy. However, existing research lacks a comprehensive and systematic investigation of the cement-coral powder-metakaolin ternary system. In this study, the hydration and rheological behavior, micromechanical and mechanical properties, and pore structure evolution of the ternary system are systematically investigated to uncover the synergistic mechanism between metakaolin and coral powder. The results indicated that, based on hydration, rheology, and mechanical properties, the recommended proportions of cement, coral powder, and metakaolin are 75 %, 10 %, and 15 %, respectively. The combination of coral powder and metakaolin effectively promotes hydration. Furthermore, it accelerates the aluminate reaction, resulting in a stronger aluminate exothermic peak immediately. In addition, metakaolin reacts with coral powder to form carboaluminate, activating the activity of the coral powder, which in turn improves the mechanical properties and pore structure of the ternary system. Moreover, metakaolin undergoes a pozzolanic reaction with calcium hydroxide, which contributes to optimizing the pore structure of the ternary system and enhancing its mechanical properties. Additionally, coral powder promotes the conversion of monosulfate to carboaluminate while inhibiting the transformation of ettringite into monosulfate. The Herschel-Bulkley model accurately simulates the dynamic rheological behavior of the ternary system. This study is highly significant and practically valuable for transforming waste coral powder into a supplementary cementitious material for the construction of the far-sea projects, providing a scientific basis for future related studies.

Techno-environmental optimal sizing and dynamic behavior of a hybrid system feeding a large-scale SWRO desalination system: The case of Djerba Island, Tunisia

Techno-environmental optimal sizing and dynamic behavior of a hybrid system feeding a large-scale SWRO desalination system: The case of Djerba Island, Tunisia

A multi-theoretical approach to supply chain management

The article examines the supply chain as a modeling object. The multi-criteria and contradictory goals in supply chain management are: on the one hand, the maximum level of service, on the other hand, minimizing logistics costs. Solving strategic optimization problems for this class of objects using classical optimization methods is difficult. The theoretical and methodological basis of the supply chain was considered from the perspective of a set-theoretic approach. The purpose of the study is to analyze the behavior of many different agents (suppliers, clients, etc.) with different needs and goals when making decisions. An agent is an active element of the system, possessing a certain autonomy and the ability to make independent decisions, relying on the information it has about the state of the environment and the actions of other agents. In turn, supply chains are a complex organizational (active) system, i.e. associated with human participation. The study of behavioral aspects and interorganizational interaction, the formation of new organizational forms are an extremely important aspect in the management and modeling of supply chains, a factor in the dynamic behavior of the logistics system. The conducted research represents an important contribution to the development of knowledge about the application of the set-theoretic approach in supply chain management. It demonstrates the applicability of this approach in practice through an analysis of a specific company, LLP «Knauf», on the Kazakhstan market.

A novel technique to detect and mitigate harmonic during islanding in grid connected PV system

The integration of photovoltaic (PV) systems into the power grid has become increasingly prevalent, providing sustainable and renewable energy solutions. However, the occurrence of islanding events, where a portion of the PV system operates independently from the main grid, presents challenges in maintaining power quality. This research paper investigates the harmonic distortions during islanding in grid-connected PV systems and proposes effective mitigation strategies. The study employs advanced simulation tools to analyse the dynamic behavior of the PV system during islanding scenarios, focusing on the occurrence and characteristics of harmonics. A detailed investigation into the root causes of harmonic distortions is conducted, considering factors such as grid fluctuations, inverter operation, and system impedance. Based on the findings, this paper introduces novel harmonic mitigation techniques tailored for islanding conditions. These techniques encompass advanced control algorithms, filter designs, and modulation strategies to suppress harmonics and enhance the overall system performance during islanded operation. Comparative assessments of different mitigation approaches are presented, evaluating their effectiveness in minimizing harmonic distortions and maintaining grid code compliance. The research contributes valuable insights to the field of grid-connected PV systems, offering a comprehensive understanding of harmonic issues during islanding events and proposing innovative solutions for their mitigation. The outcomes of this study are crucial for advancing the reliability, stability, and power quality of PV systems that are connected to the grid, which makes it possible for green energy sources to be added to the grid without any problems.

Study of the Influence of the Relative Rigidity of an Elastic Hybrid System Without Damping, on Natural Self-Pulsation, Amplitude and Dynamic Factor Due to Forced Vibration

Abstract The paper aims to study the dynamic behavior of a hybrid elastic system without damping consisting of a beam in a cantilever supported on helical compression springs on which an electric motor is mounted. With the help of the MATHCAD professional program, the influence of the relative stiffness of the elastic bar subjected to bending and the springs subjected to compression was simulated, on the natural pulsation, the amplitude of the vibrations and the dynamic factor of the forced vibrations for two assembly variants of the electric motor

Hamilton energy, competitive modes and ultimate bound estimation of a new 3D chaotic system, and its application in chaos synchronization

Abstract This paper discusses the dynamical behavior of a new 3D chaotic system of integer and fractional order. To get a comprehensive knowledge of the dynamics of the proposed system, we have studied competitive modes and Hamilton energy for different parameter values. In order to get the ultimate bound set for the proposed system, we employed the Lagrange coefficient approach to solve the optimization problem. We have also explored the use of the bound set in synchronization. Furthermore, we have examined the Hamilton energy, time series, bifurcation diagrams, and Lyapunov exponents for the fractional version of the proposed chaotic system. Finally, we looked at the Mittage-Leffler positive invariant sets and global attractive sets by merging the Lyapunov function approach with the Mittage-Leffler function. Numerical simulations have shown the obtained bound sets and other analytical outcomes.

Study of the Influence of the Dynamic Absorber on the Natural Pulsation of the Forced Vibration of an Electric Motor Mounted on a Cantilever Beam Subjected to Bending and Supported on Two Helical Compression Springs

Abstract The paper aims to study the dynamic behavior of an elastic mechanical system without damping consisting of two masses m1 and m2 mounted on a cantilever beam subjected to bending and supported on two helical compression springs, or the influence of the dynamic mass absorber m2 on the pulsation characteristics of the forced bending vibrations of the mass electric motor m1. Using the MATHCAD professional program, the influence of the mounting method of the dynamic absorber on the elastic system's own pulsations can be determined.

A Dual-Iterative Meshing Stiffness Model and Vibration Analysis for an Angular Misaligned Helical Gear Pair Considering Misalignment-Induced Contact Line Variation

Abstract Angular misalignment is a common error in gear transmission systems, significantly altering the contact and dynamic behaviors of the gear system. Conventionally, the time-varying mesh stiffness (TVMS) of helical gear pairs with angular misalignment is estimated under the assumption of a uniform load distribution along a fixed contact line. However, this simplification neglects the variations in contact line length and load distribution due to angular misalignment, thereby compromising the accuracy of TVMS predictions. To address this limitation, we propose a novel dual-iterative model for TVMS calculation in helical gears, accounting for the angular misalignment-induced contact line variation. This model combines traditional iterative calculations for gear slices with an additional iterative loop for the misalignment-induced contact line changes. Furthermore, it considers both axial and tangential meshing stiffnesses. The proposed dual-iterative TVMS model is verified by using the finite element (FE) method. Moreover, a six degree-of-freedom (DOF) dynamic model for misaligned helical gears is established to investigate the effects of misalignments on the vibration characteristics of the gear pair. An experimental setup utilizing a back-to-back helical gear test rig with adjustable angular misalignment is constructed to validate the proposed model. The experimental results exhibit a close alignment with the simulation predictions. It is concluded that the proposed model is suitable for estimating the TVMS and dynamic analysis of helical gear pairs with angular misalignment errors.

The assembly and dynamics of ecological communities in an ever‐changing world

AbstractAlternative perspectives on the maintenance of biodiversity and the assembly of ecological communities suggest that both processes cannot be investigated simultaneously. In this concept and synthesis, we challenge this view by presenting major theoretical advances in structural stability and permanence theory. These advances, which provide complementary views, allow studying the short‐ and long‐term dynamics of ecological communities as changes in species richness, composition, and abundance. Here, the global attractor, technically named informational structure (IS), is the central element to construct from information of species' intrinsic growth rates and their strength and sign of interactions. The global attractor has four main properties: (1) It contains all the limits of what is feasible and unfeasible of the dynamical behavior of an ecological system, therefore, (2) it provides a thorough characterization of all combinations of species' richness and composition in which species can coexist (i.e., feasible and stable equilibrium), (3) as well as all connections (paths) of assembly between coexisting communities. Importantly, (4) such topology of coexisting communities and their connections changes when environmental (abiotic and biotic) variation affects the ability of species to grow and interact with others. Overall, these four properties allow switching from a traditional evaluation of species coexistence at equilibrium to a much more realistic nonequilibrium perspective where changes in the structure of the global attractor underlie the transient ecological dynamics. Several fields in ecology can benefit from the study of an IS. For instance, it can serve to evaluate community responses after the end of a perturbation, to design restoration trajectories, to study the consequences of biological invasions on the persistence of native species within communities, or to assess ecosystem health status. We illustrate this latter possibility with empirical observations of 7 years in Mediterranean annual grasslands. We document that extremely wet or dry years generate ISs supporting few coexisting communities and few assembly paths. The remaining communities distinguish winners from losers of ongoing climate change and indicate the limits to future community assembly opportunities. A fully tractable operational framework is readily available to understand and predict the assembly and dynamics of ecological communities in an ever‐changing world.

Experimental investigation of particle impact dampers: Vibration reduction and noise levels with varied particle numbers

Structural vibrations present significant challenges in engineering systems, and particle impact dampers (PIDs) have emerged as a promising solution for vibration control. This paper presents a comprehensive experimental investigation on the damping performance of PIDs with varying numbers of particles. The experimental setup involves subjecting a single-degree-of-freedom (SDOF) structure to base motion excitations. Frequency response analysis is conducted to assess the dynamic behavior of the primary system using different PID designs. PIDs with one mass, two masses, three masses and multiple particles are designed and analyzed using the same mass ratio. Additionally, time domain displacement responses of the top of the structure and the base are measured to capture the system's response characteristics. The frequency response analysis reveals the influence of different particle configurations on the system's response amplitude at various frequencies. Interestingly, the results show that a PID with multiple particles exhibits reduced damping performance due to excessive particle-particle collisions. These collisions decrease the energy of the particles, leading to lower velocity before impact. This highlights that the impact itself is the primary source of damping in PIDs, and any other phenomena, such as particle-particle collisions, directly affect the relative velocity before impact. The outcomes demonstrate that an optimal design of PID can reduce vibration amplitude by approximately 85 % with single mass, two masses, and three masses configurations. Conversely, the best-case scenario of PID with multiple particles provides a vibration amplitude reduction of 75 % compared to the absence of a damper. Furthermore, noise data is recorded for all cases, as noise generation is a significant concern associated with PIDs. The results indicate noise magnitudes of 62.5 dB, 70.60 dB, 73.24 dB and 78.64 dB for PIDs with single mass, two masses, three masses, and multiple particles, respectively. Overall, the relationship between the number of particles and damping performance provides valuable insights for optimizing PID designs and ensuring comfortable operation. The findings have broad implications for diverse engineering systems, leading to improved structural performance, reduced noise, and enhanced safety. This study could serve as the basis for several potential applications of PID in structural vibration control with enhanced performance and reduced noise.

Dynamical Phenomena Based on Chaotic Systems Without Equilibria

A chaotic system without equilibrium points is a focal subject in recent years, and its unique dynamic characteristics have attracted extensive research. In this paper, different chaotic systems with no equilibrium points are constructed by modifying the Sprott-A system. The test results show that the first system is conservative. After investigating the hidden dynamical behavior of the first system, the rotation attractor phenomenon is revealed by the rotation factor. Next, we make a second transformation of the Sprott-A system. By introducing a trigonometric function, we get a new system that can generate infinitely many coexisting grid attractors. After calculation, we find that the new system still belongs to the chaotic system without equilibrium points and the coexistence phenomenon of attractors is created by adjusting the initial value continuously. The chaotic system without equilibrium points which can realize the coexistence of attractors has potential applications in some related fields, which is worthy of further study.

Prototype data analysis of the dynamics of the Venice gate-barriers during an extreme storm event

The MoSE barriers system was designed and constructed at the inlets of the Venice Lagoon (Italy) in order to limit and tame the flooding events in the Lagoon areas and in the City. The success of the design and operation of the system has been demonstrated by the significant reduction in the number and intensity of floods in the lagoon since its beginning of operations in 2020. In this study, we investigate the dynamical behavior of the MoSE system at full-scale by analyzing the barriers behavior during the severe storm event of November 22nd, 2022. In particular, the dynamical response of the Chioggia barrier to waves and storm surge is studied in detail. Spectral analysis of field records, barrier and inlet modal analyses and Empirical Orthogonal Functions (EOF) techniques are applied to provide a key for interpreting the actual behavior of such a complex system during a storm event, highlighting dominant frequencies and checking for the occurrence of resonance phenomena. First, a brief review of the experimental and theoretical studies carried out over the past forty years is given. Modal patterns of gates oscillations detected via EOF analysis confirm the presence of the eigenmodes of both the barrier and the inlet; however, the gates oscillations during the considered event are mild and the hydraulic performances of the system are satisfactory for the severe event studied. Further field measurements and future severe events should be studied to reach extended conclusions.

Some Bifurcations of Codimensions 1 and 2 in a Discrete Predator–Prey Model with Non-Linear Harvesting

This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model.

Polyester mooring system design and evaluation of a semi-platform in south China sea

Polyester rope offers numerous advantages over traditional steel catenary mooring systems and is considered an appealing option for deep-water mooring systems. In this paper, the design and evaluation procedure of the polyester mooring system for a semi-submersible platform located in the South China Sea is presented. A fully coupled numerical model of the semi-submersible platform, including all risers and mooring lines, has been established and calibrated through wave basin testing. To simulate the elongation behavior of polyester, a static-dynamic stiffness model is employed, and the corresponding procedure for mooring evaluation is established to simulate the mooring response under extreme environmental conditions. A comprehensive fatigue analysis is also conducted for the polyester mooring system using time domain dynamic theory. The effects of Vortex-Induced Motion (VIM) on mooring fatigue damage are also considered. The results indicate that the polyester mooring system could be safely operated at the target offshore field throughout its service life. Additionally, model test calibration is a crucial procedure during the entire mooring evaluation process, and the numerical model should be adjusted appropriately to accurately reflect the dynamic behavior of the coupled system. This study also illustrates that the stiffness of the rope plays a crucial role in polyester mooring design and global performance calculations. The proposed evaluation methodology can provide a foundation for the design of polyester mooring systems and for evaluating their safety and reliability in engineering practice.