Analysis Of Dynamical Systems Research Articles

Dynamical system analysis of DBI scalar field cosmology in coincident $f(Q)$ gravity

Abstract In this article, we offer the dynamical system analysis of the DBI (Dirac-Born-Infeld) scalar field in a modified $f(Q)$ gravity context. We have taken a polynomial form of modified gravity and used two different kinds of scalar potential, i.e., polynomial and exponential, and found a closed autonomous dynamical system of equations. We have analyzed the fixed points of such a system and commented on the conditions under which deceleration to late-time acceleration happens in this model. We have noted the similarity of the two models and have also shown that our result is indeed consistent with the previous work done on Einstein's gravity. We have also investigated the phenomenological implications of our models by plotting the EoS ($\omega$), Energy density ($\Omega$), and deceleration parameter ($q$) w.r.t. to e-fold time and comparing with the present value. Finally, we conclude the paper by observing how the dynamical system analysis differs in modified $f(Q)$ gravity, and we also provide some of the future scope of our work.

Dynamic control of pre-stressed cable systems by using frictional sliding cables

Passive dynamic control with integrated dampers is an efficient strategy for the vibration of a cable-strut system. Except the rigid components, the flexible components are also a triable direction as the integrated damper, especially for the continuous cable systems. This paper proposes a novel dynamic control method for pre-stressed cable systems by using frictional sliding cables. Firstly, a simplified dynamic simulation method is introduced. The friction of sliding cables can be considered in the dynamic analysis of a continuous cable system. Secondly, two numerical examples with sliding cables including the types of Levy and Geiger are established. The results show that frictional sliding cables can reduce the structural dynamic response. Thirdly, a dynamic experiment of a Geiger-type cable dome with sliding ridge cables is carried out. The acceleration of the structure during vibration is recorded and compared with the results of the conventional configuration. The dome with sliding cables exhibits higher damping ratios, indicating superior vibration reduction capabilities. The frictional energy dissipation of this study can be taken as a dynamic control strategy for continuous cable structures during the design and analysis process.

Qualitative analysis and new exact solutions for the extended space-fractional stochastic (3 + 1)-dimensional Zakharov-Kuznetsov equation

Abstract In this paper, the extended (3 + 1)-dimensional Zakharov-Kuznetsov equation, which describes the propagation of ion-acoustic waves in a magnetic environment, is investigated. Due to the exposure of the propagation to unpredictable factors, the stochastic model is assessed including the Brownian process, in addition to including the recent concept of truncated M-fractional derivative. A fractional stochastic transformation is applied to transform the model into an integer-order ordinary differential equation which in turn is equivalent to a conservative Hamiltonian model. Novel solutions, such as hyperbolic, trigonometric, and Jacobian elliptic functions, are established by employing both of the qualitative analysis of dynamical systems and the first integral of the Hamiltonian model. We explore and graphically display the effects of the fractional derivative order and noise intensity on the solutions structures. In the deterministic instance, i.e., in the absence of noise, solitary and cnoidal solutions among other traveling wave solutions of the Zakharov-Kuznetsov equation, are derived. Further, it is found that the curvature of the wave disturbs and the surface turns substantially flat by increasing the value of noise. While the curve in all cases loses its characteristic shape and degenerates into another deterministic shape by changing the fractional derivative order.

Effects of Unbalanced Incentives on Threshing Drum Stability during Rice Threshing

As a result of the uneven growth of rice, unbalanced vibration of threshing drum caused by stalk entanglement in combine harvester is more and more severe. In order to reveal the influence of unbalanced excitation on the roller axis locus during rice threshing, the stability of threshing drum was studied. The dynamic signal test and analysis system are used to test the axial trajectory of threshing drum. At the same time, the influence of the unbalanced excitation caused by the axis winding on the axis trajectory is analyzed by the experimental results. Axis locus rules under no-load and threshing conditions are obtained. In order to simulate the axial and radial distribution of unbalanced excitation along the threshing drum, the counterweight was distributed on the threshing drum instead of the entangled stalk. Then, the definite effect of unbalanced excitation on the rotating stability of threshing drum is analyzed. Results show that the amplitude of stem winding along the grain drum is larger in the vertical direction and smaller in the horizontal direction when compared with the unloaded state under 200 g weight. It was found that the amplitude in both horizontal and vertical directions decreased after 400 g and 600 g counterweights were added, respectively, to simulate the radial distribution of stalk winding along the grain barrel. Finally, it can be seen that with the increase in the weight of the counterweight, the characteristics of the trajectory misalignment of the threshing cylinder axis become more and more obvious. This study can provide reference for reducing the unbalanced excitation signal of threshing drum and improving driving comfort.

Static and dynamic analysis of a new offshore wind turbine system supported with outriggers

This article presents an innovative structural system for offshore wind turbines supported on monopiles. The novelty of this system lies in its enhancement of the lateral stiffness of the tubular tower through the incorporation of an outrigger system, widely employed in high-rise buildings. This novel system is modeled as a Timoshenko beam-column element under both static and dynamic loading scenarios, incorporating geometric nonlinearity and accounting for the effect of soil-structure interaction. A comprehensive numerical analysis was conducted to evaluate the system’s behavior under various static and dynamic load cases, utilizing soil data from the Red Sea region of Egypt. A modal analysis is also incorporated to investigate the eigenmodes of the proposed system. This study offers valuable insights for designers and researchers, providing guidelines and diagrams for the implementation of the proposed system.

Applying Zero-Crossing Method for Frequency Map Analysis of Dynamical Systems

Abstract We present a simple method for estimating fundamental frequencies from orbit’s time series of triaxial dynamical systems based on the zero-crossing technique. The simplicity and high performance of the method make it a viable alternative to more advanced, but rather complex and computationally expensive techniques based on Fourier spectral analysis and iterative torus-mapping with action-angle variables. More importantly, the method provides a simple and quick way to identify irregular orbits and quantify their level of chaoticity, allowing to detect even a subtle onset of chaos. To validate the proposed algorithm, we performed comparison tests with synthetic quasi-periodic signals and with other methods using the triaxial Dehnen potential. We found noticeable differences in frequency maps constructed with our method and methods based on Fourier spectral analysis that we attributed to the way we assign static properties to chaotic orbits. At the same time, our frequency maps turn out to be in very good agreement with the maps obtained using the action-based technique.

Telemetry to solve dynamic analysis of a distributed system

In the modern software development world, implementing distributed solutions has become quite common due to the flexibility it brings to big companies. The downside is that when developing such systems, especially in many teams, global design problems may not be obvious and lead to a slowdown in the development process or even problems with the location of errors or degradation of overall system performance. In addition, the timely reaction to system degradation is complicated by the distributed nature of the architecture; while manually configuring rules for reporting problematic situations can be time-consuming and still incomplete, automatic detection of possible system anomalies will give engineers (especially Software Reliability Engineers) the focus on problems. For this reason, applications that can dynamically analyse the system for problems have great potential. Currently, the topic of using telemetry for system analysis is actively studied and gaining traction, so further research is valuable. The work aims to theoretically and practically prove the possibility of using telemetry to analyse a distributed information system and detect harmful architectural practices and anomalous events. To do this, firstly, a detailed overview of the problems related to the topic and the feasibility of using telemetry is provided; the next section briefly describes the history of the development of monitoring systems and the key points of the latest OpenTelemetry standard, reviews popular application performance monitoring systems, and defines innovative features to be further researched. The main part includes an explanation of the approach used to collect and process telemetry, a reasoning behind the usage of Neo4j as a data storage solution, a practical overview of graph theory algorithms that help in the analysis of the collected data, and a description outlining how the PCA algorithm is employed to detect unusual situations in the whole system instead of individual metrics. The results provide an example of using the software presented with Neo4j Bloom to visualise and analyse the data collected over several hours from the OpenTelemetry Demo test system. The last section contains additional remarks on the results of the study.

Dynamical Modeling and Dynamic Characteristics Analysis of a Coaxial Dual-Rotor System

The dual-rotor structure is the primary excitation source of aero-engine vibration. It is essential to study the dynamical model and analyse the dynamic characteristics such as critical speed and the unbalanced response for rotor system dynamics. The coaxial dual-rotor support scheme of an aero-engine was introduced in the previous work, and the physical model with a high-speed flexible inner rotor of a sizeable length-diameter ratio has been designed. Then a finite element dynamic model based on the Timoshenko beam elements and rigid body kinematics of the dual-rotor system is modelled, with the Newmark-β method and Newton-Raphson method used for the numerical calculation to study the dynamic characteristics of the system. Three different simulation models, including beam-based FE (1D finite element) model, solid-based FE (3D finite element) model, and TM (transfer matrix) model, were designed to study the characteristics of mode and the critical speed characteristic of the dual-rotor system. The unbalanced response of the dual-rotor system was analysed to study the influence of mass unbalance on the rotor system. The effect of different disc unbalance phases and different speed ratios on the dynamic characteristics of the dual-rotor system were investigated in detail. The experimental result shows that the beam-based FE model is effective and suitable for studying the dual-rotor system. Conflict of Interest Statement The authors declare no conflicts of interest.

Analysis and Control of Partially Observed Discrete-Event Systems via Positively Constructed Formulas

This paper establishes a connection between control theory for partially observed discrete-event systems (DESs) and automated theorem proving (ATP) in the calculus of positively constructed formulas (PCFs). The language of PCFs is a complete first-order language providing a powerful tool for qualitative analysis of dynamical systems. Based on ATP in the PCF calculus, a new technique is suggested for checking observability as a property of formal languages, which is necessary for the existence of supervisory control of DESs. In the case of violation of observability, words causing a conflict can also be extracted with the help of a specially designed PCF. With an example of the problem of path planning by a robot in an unknown environment, we show the application of our approach at one of the levels of a robot control system. The prover Bootfrost developed to facilitate PCF refutation is also presented. The tests show positive results and perspectives for the presented approach.

Dynamic analysis of multi-DOF acoustic resonant system involving highly viscous fluids based on fluid-structure interaction

This paper investigates the dynamic characteristics of a multi-degree-of-freedom (multi-DOF) acoustic resonant system involving highly viscous fluids. First, a fluid-structure interaction (FSI) model is established to describe the interaction between the multi-DOF acoustic resonant system and the two-phase fluids, and then the effects of various excitation parameters on the dynamic response of the coupled system are studied. Under the influence of vertical acoustic vibration, the fluid in the container undergoes violent and irregular motions, which leads to a decrease and fluctuation in the equivalent mass of the fluid. The reduction in fluid equivalent mass causes the excitation frequency to deviate from the natural frequency of the multi-DOF acoustic resonant system, thus significantly reducing the dynamic response of the coupled system. Furthermore, the fluctuation of the fluid equivalent mass induces a quasi-periodic motion pattern of the acoustic resonant system. Although increasing the excitation amplitude can effectively increase the dynamic response of the coupled system, it can also increase the fluctuation level of the dynamic response to a certain extent. By appropriately increasing the excitation frequency, the coupled system can operate at a new resonant frequency, thereby reducing the influence of fluid motion on the dynamic response of the system.

Kalman filter based on a fractional discrete-time stochastic augmented CoVid-19 model

In this paper, we study the dynamics of the CoVid-19 outbreak in Semarang, Indonesia, using a fractional CoVid-19 model. We first determine the effects of the isolation rate ∊ and infection rate β on the reproduction number R0 and infected number V. We find that R0 is directly proportional to β and inversely proportional to ∊. For V, the effect of physical distancing is not as significant as changing ∊. As ∊ increases, V decreases, the number of susceptible individuals increases, the number of quarantined individuals decreases sharply, and the number of recovered individuals decreases. Moreover, the effect of vaccination is also considered. The combination of physical distancing, isolation, and vaccination has a significant impact on reducing the number of infected individuals. Analysis of dynamical systems allows us to understand the characteristics of our model, such as its boundedness and non-negativity, the existence of equilibrium points, the existence and uniqueness of solutions, and the local and global stability. To validate our fractional CoVid-19 model, we introduce the fractional extended Kalman filter (FracEKF) as a prediction method and compare the results against reported CoVid-19 data. FracEKF is a modified version of the basic extended Kalman filter with a time-fractional memory effect. The prediction results illustrate the accuracy of this model in terms of the root mean square error (RMSE), normalized root mean square error (NRMSE), and mean absolute percentage error (MAPE) for each fractional-order. Varying ∊ reproduces the trends observed in the reported data for the number of infected individuals, i.e., when ∊ increases, the infected number decreases. Moreover, a higher fractional-order results in higher model accuracy. Furthermore, higher values of the process noise Qf give smaller errors, whereas higher values of the observation noise Rf produce higher errors. Qf and the fractional-order α are inversely proportional to RMSE,NRMSE, and MAPE, whereas Rf is directly proportional to RMSE,NRMSE, and MAPE.

Dynamic analysis and multi-objective optimization of solar and hydrogen energy-based systems for residential applications: A review

This paper examines the potential of solar and hydrogen (H2) energy-based hybrid energy systems for residential applications. The growing need for energy and the demand for sustainable energy sources have led to the development of integrated energy systems that combine renewable energy resources to meet energy needs. This paper overviews recent studies on hybrid energy systems for on-grid and off-grid residential utilizations. It discusses the system configuration and components of hybrid energy systems, including solar panels, electrolyzers, fuel cells (FC), and batteries. It also covers the technical optimization of integrated energy systems, including sizing, control strategies, and economic analysis. The key findings of this review paper indicate that hybrid energy systems can offer dependable and sustainable energy for residential applications. Through numerical analyses, the optimal dimensioning of the system elements and control strategies can significantly enhance the system's performance and lower the cost of energy. This study also highlights the challenges and opportunities for integrating hybrid energy systems within residential applications. Overall, it provides in-depth perspectives on the possibilities inherent in solar and hydrogen energy-based hybrid energy systems for residential applications. The findings can guide future research and the advancement of hybrid energy systems for sustainable energy solutions.

Averaging principles for multiscale stochastic Cahn–Hilliard system

In this paper, we will establish averaging principles for the multiscale stochastic Cahn–Hilliard system. The stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. Under suitable conditions, two kinds of averaging principle (the autonomous case and the nonautonomous case) are proved, and as a consequence, the multiscale system can be reduced to a single stochastic Cahn–Hilliard equation (averaged equation) with a modified coefficient, the slow component of multiscale stochastic Cahn–Hilliard system towards to the solution of the averaged equation in moment (the autonomous case) and in probability (the nonautonomous case).

Dynamic simulation and analysis of dichloromethane-acetone, dichloromethane-trichloromethane and dichloromethane-toluene VOC mixture abatement systems under transient feed conditions

Minimisation of environmental footprint in line with sustainability goals rests at the top of the agenda of the pharmaceutical industry. Volatile Organic Compounds (VOCs), while essential to primary pharmaceutical manufacturing, are solvents whose emissions pose a risk to human health and ecosystems. Adsorption on activated carbon beds is an established technology for end of pipe emissions control, which, however, faces efficiency limitations by quick and irregular bed saturation due to complex, transient feeds. This study employs a validated nonisothermal, multicomponent adsorption model to quantitatively assess the exact effect and potential value of waste stream feed sequencing towards activated carbon bed utilisation optimisation. Our results indicate that gradual increase of dichloromethane feed concentration in combination with a low, constant inlet concentration of the strongly adsorbing component leads to the latest breakthrough onset for the dichloromethane-acetone, dichloromethane-chloroform and dichloromethane-toluene mixtures, paving the way to industrial VOC emission abatement scheduling and process optimisation.

A novel and efficient Hamiltonian dynamic analysis approach for constraint force determination in flexible multibody systems

In the dynamic analysis of flexible multibody systems, Hamiltonian formulations offer advantages in numerical stabilization and systematic handling of systems with varying mass. However, current approaches face challenges. Differential algebraic equations (DAEs) can directly express constraint forces but are computationally inefficient, while ordinary differential equations (ODEs) are more computationally efficient but cannot directly represent constraint forces due to the elimination of the Lagrange multiplier. This paper presents an innovative and efficient dynamic analysis approach based on the Hamiltonian formulation, incorporating velocity transformation and open-constraint coordinate methods. Compared to conventional DAE-based Hamiltonian formulations, our approach conducts analysis efficiently using only independent variables. Compared to conventional ODE-based Hamiltonian formulations, our approach effectively expresses constraint forces through Lagrange multiplier reformulation. Furthermore, when compared to the traditional ODE-based Lagrangian formulation, our approach exhibits superior computational efficiency. Numerical simulations assess our proposed formulation, showing agreement with conventional formulations, shorter calculation time, and alignment with analytical results, confirming the accuracy and usefulness of our approach.

Dynamic Analysis and Field-Programmable Gate Array Implementation of a 5D Fractional-Order Memristive Hyperchaotic System with Multiple Coexisting Attractors

On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke dimension, and equilibrium stability of the chaotic model are studied. Subsequently, we explore the construction of the 5D FOMHS, introducing the definitions of the Caputo differential operator and the Riemann–Liouville integral operator and employing the Adomian resolving approach to decompose the linears, the nonlinears, and the constants of the system. The complex dynamic characteristics of the system are analyzed by phase diagrams, Lyapunov exponent spectra, time-domain diagrams, etc. Finally, the hardware circuit of the proposed 5D FOMHS is performed by FPGA, and its randomness is verified using the NIST tool.

Optimizing energy storage plant discrete system dynamics analysis with graph convolutional networks

Addressing the challenges of suboptimal model performance and excessive parameters and operations in the optimization of energy storage power plants utilizing Graph Convolutional Network (GCN), this paper introduces a novel approach – the packet-switched graph convolutional network. Initially, a GCN extreme learning machine is established. Drawing inspiration from this solid foundation, we have innovatively crafted a group exchange graph convolution module. This module leverages group graph convolution techniques to amalgamate unique node feature information, tailored to diverse topology graph matrices based on various groupings. This innovative approach ensures that information flows freely and effectively among distinct groupings. Furthermore, we have designed a cutting-edge timing depth separation convolution module, comprising two innovative components. The first component introduces timing depth separation convolution, revolutionizing the original timing convolution module. The second component, the packet-switching graph convolutional network, revolutionizes the time sequence depth separation convolution process. It achieves this by employing 1 × 1 convolutional layers between different feature fusion packets, enabling seamless information exchange between distinct packets. Experimental results demonstrate the efficacy of the proposed model, with root mean square error (RMSE) metrics and root mean square error (MAE) metrics for single-step prediction reaching 46.08 and 26.22 at 60 min, respectively. In multi-step testing, the proposed model exhibits a 14.71 % reduction in RMSE error at the 15-min scale and a 9.29 % reduction at the 60-min scale compared to the benchmark model. This performance improvement enhances the operational efficiency and reliability of the energy storage plant, particularly under dynamic changes in the time series.

Ghost dark energy in Tsallis and Barrow cosmology

According to the thermodynamics-gravity conjecture, any modification to the entropy expression leads to the modified cosmological field equations. Based on this, we investigate the cosmological consequences of the modified Friedmann equations when the entropy associated with the horizon is in the form of Tsallis/Barrow entropy and the dark energy (DE) component is in the form of ghost dark energy (GDE). We perform a dynamical system analysis and see that the Tisallis GDE(TGDE) and Barrow GDE(BGDE) can exhibit a correct phase space evolution for suitable range of the free parameters(0<Δ<1 for BGDE and β<3/2 for TGDE). We find that in BGDE and TGDE (with Q=3b2H(ρD+ρm)), there exist an early radiation dominated phase of expansion which is absent for GDE model in standard cosmology. It is worth mentioning that seeking an unstable phase of matter dominated in TGDE leads to a new constraint on β (<3/2). Using the resulting range of free parameters from latter step we find that both models are capable to explain the cosmic evolution from deceleration to an accelerated phase. We observe that increasing Δ (β) parameters leads to a delay in the cosmic phase transition. We conclude that BGDE and TGDE are viable cosmological models which predict a consistent phase transition of the cosmic expansion for suitable ranges of the parameters. We also calculate the squared sound speed for both models and find out that they are unstable against perturbations. Next, we proceed the statefinder analysis and see that both models are significantly distinct from ΛCDM as well as with respect to each other at past epochs, while both of them catch the standard cosmology at far future. We also explore the impacts of the non-extensive parameters on the density perturbations and find out that the pattern of density contrast (δ) evolution in TGDE/BGDE is distinct from GDE in standard cosmology.

A mathematical introduction to complex dynamical systems

This work proposes an investigation of the theory of dynamic systems, focusing on the analysis of entropy in its classical and topological manifestations. Initially, the fundamental concepts of dynamical systems theory are presented, with an emphasis on topological dynamical systems (TDS). Next, definitions of discrete topological entropy and its relationship to dynamical systems are discussed, followed by the introduction of topological entropy pressure as a weighted form of topological entropy. Subsequently, some applications of topological entropy in dynamic systems are examined, highlighting its role in the analysis of chaotic systems and in ergodic theory. Furthermore, we present a new theory, called Topological Ergodic Entropy Theory (TEET), which offers an innovative approach to the analysis of ergodic dynamical systems. Finally, the Ergodic Theory of Turbulent Flow (ETTF) is introduced, exploring the relationship between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. The results presented contribute to a deeper understanding of the complexity of dynamical systems and their applications in various areas of mathematics and physics. The investigation of topological entropy and its applications in dynamical systems offers new insights into the chaotic and stochastic behavior of these systems, while the introduction of new theories, such as ETTF, provides a new perspective for the analysis and modeling of turbulent phenomena.

Modeling insect growth regulators for pest management.

Insect growth regulators (IGRs) have been developed as effective control measures against harmful insect pests to disrupt their normal development. This study is to propose a mathematical model to evaluate the cost-effectiveness of IGRs for pest management. The key features of the model include the temperature-dependent growth of insects and realistic impulsive IGRs releasing strategies. The impulsive releases are carefully modeled by counting the number of implements during an insect's temperature-dependent development duration, which introduces a surviving probability determined by a product of terms corresponding to each release. Dynamical behavior of the model is illustrated through dynamical system analysis and a threshold-type result is established in terms of the net reproduction number. Further numerical simulations are performed to quantitatively evaluate the effectiveness of IGRs to control populations of harmful insect pests. It is interesting to observe that the time-changing environment plays an important role in determining an optimal pest control scheme with appropriate release frequencies and time instants.