Global Stability Research Articles

Numerical analysis on global stability performance of fold-fastened multi-cellular steel walls

As a novel cold-formed steel (CFS) built-up closed member, the global stability performance of fold-fastened multi-cellular steel wall (FMSW) under axial compression was numerically investigated in this paper. Firstly, finite element (FE) models of FMSWs that could precisely simulate the global buckling were developed using ABAQUS and validated by existing experiments of CFS built-up members. Then, eight groups of numerical examples were analyzed to explore the effect of different parameters on the global stability performance of FMSWs, including the geometrical dimensions, material property, indented spacing and initial imperfection, where the corresponding global stability coefficients (φ) of FMSWs could be obtained from FE results. The normalized slenderness ratio (λn) of FMSWs was calculated based on the concept of the effective width method (EWM). Finally, the FE results of (φ, λn) were compared with existing stability design curves of steel structures in various codes. It was found that the stability design curve-d specified in Chinese code GB 50017–2017 could achieve a conservative design, and it could provide a valuable reference for designing slender FMSWs in practice.

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Global exterior stability of the Minkowski space: Coupled Einstein–Yang–Mills perturbations

Here we prove a global gauge-invariant radiation estimates for the perturbations of the 3 + 1 dimensional Minkowski spacetime in the presence of Yang–Mills sources. In particular, we obtain a novel gauge invariant estimate for the Yang–Mills fields coupled to gravity in a double null framework in the Causal complement of a compact set of a Cauchy slice. A consequence of our result is the global exterior stability of the Minkowski space under coupled Yang–Mills perturbations. A special structure present both in the null Bianchi equations and the null Yang–Mills equations is utilized crucially to obtain the dispersive estimates necessary to conclude the global existence property. Direct use of Bel-Robinson and Yang–Mills stress-energy tensor to obtain the energy estimates is avoided in favor of weighted integration by parts taking advantage of the manifestly symmetric hyperbolic characteristics of null Bianchi and null Yang–Mills equations. Our result holds for any compact semi-simple gauge group. This is the first stability result of Minkowski space including a non-linear source.

Modified Nested Saturated Control for Uncertain Multiple Integrators With High-Order Nonlinear Perturbation.

This article studies the global asymptotic stability problem of multiple integrators subject to uncertain parameters and high-order nonlinear perturbation. By introducing a modified saturation function with positive tunable parameters, three types of modified nested saturated controllers with different parameter assignments are proposed to handle the uncertain integrators with high-order nonlinear perturbation. The specific mechanism of the modified nested saturated controllers with different parameter assignments, in which control parameters appear before states, saturation functions, or saturation levels, is comprehensively analyzed. With the help of a modified saturation function, the global convergence domain of each state can be kept invariable in the saturation reduction analysis. Meanwhile, a large saturation level is obtained by adjusting positive tunable parameters. Combining with derivatives calculation and M -matrix-based comparison theory, proposed saturated control schemes are utilized to handle the considered system. Finally, an active magnetic bearing (AMB) system is revisited as an uncertain mechanical system and used to verify the feasibility of the proposed control designs.

Anti-unwinding adaptive robust backstepping attitude maneuver control for rigid spacecraft

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft.

Physical interpretation on development and validation of the reaction routes of complex chemical kinetic model

Simulating the complexity in its entirety proves highly challenging, to examine both the local and global stability of the model, as well as its positivity, recognizing the overall instability. To address this challenge, a strategy of splitting down the multi-route complex reactions into its independent sub-routes is employed. For the validation of sub-routes, the stability and positivity of each individual route were comprehensively analyzed. In addition, we employ techniques to simplify our models by considering factors such as reaction speed and thermodynamic properties, ensuring their accuracy. Furthermore, we integrate the Spectral Quasi-Equilibrium Manifold to obtain a deeper understanding of the sequential advancement of reactions, focusing on the slowest eigenvector. A comprehensive examination of the mathematical underpinnings of these reaction steps and diverse pathways is conducted. We also investigate the temporal behavior of these pathways, yielding fresh perspectives. Our findings suggest the feasibility of independently evaluating each pathway rather than treating the entire mechanism as a singular entity. To enhance our analysis, we conduct a local sensitivity assessment using the SimBiology toolbox in MATLAB of each route and compare calculation periods for TRM (Total Relative Motion). Furthermore, we employ the short-time Fourier transform graph to capture time–frequency information regarding the steady state of compounds in various routes, revealing spectral variations over time.

Entirely Coupled Recurrent Neural Network-Based Backstepping Control for Global Stability of Power System Networks

In an interconnected power system network, global performance is affected by various unknown power system parameters subjected to system uncertainties. These unknown parameters in the control expression deteriorate the performance of the power system network. Therefore, these terms associated with the control expression must be estimated precisely. This paper proposes an adaptive backstepping scheme using an entirely coupled recurrent neural network (ECRNN) to estimate these control terms. Three continuous differentiable functions are used to design control input, virtual signals, and adaptive control laws to achieve global performance. The objective of ECRNN is to reduce the control complexity by estimating the associated nonlinear term in the control expression. It will facilitate the complex formulation of the controller and improve system performance. The robust functional estimation ability of ECRNN will make the system immune to uncertainties that may appear due to external disturbances. In ECRNN, feedback loops are added to each neuron layer to achieve additional estimation accuracy. The proposed adaptive law enhances the online weight update speed and accuracy. Verification of the proposed scheme is carried out in MATLAB/Simulink. It is also verified in the real-time digital simulator (RTDS) platform using the IEEE standard New England 39-bus, 10-machine power system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the existing limitations in the global performance of a multimachine power system network due to uncertainty in the system parameters. Uncertainties in the power system network primarily appeared due to penetration of renewable power sources, load uncertainty, or occurrence of an uncertain fault in the network. As power system networks are complex nonlinear interconnected systems, these perturbations in the generator states may cause economic losses, load demand uncertainty, or electric scarcity. Thus, a control scheme is required to address the global performance of such networks. This article proposes uniform ultimate bounded stability of synchronous generators in a multimachine power system network with a robust ECRNN-based backstepping control design. The other available technique has not adequately addressed the global performance under uncertainties. The efficacy of the proposed scheme is verified in a real-time environment via a real-time digital simulator which may be a feasible solution for designing excitation control for the synchronous machine in an extensive industrial network.

Co-infection dynamics between HIV-HTLV-I disease with the effects of Cytotoxic T-lymphocytes, saturated incidence rate and study of optimal control

The spreading of HIV or HTLV-I among the cells has received the great attention in recent modelling study to explore the virus infection dynamics. The co-infection of HIV and HTLV-I with the effect of Cytotoxic T-lymphocytes (CTLs) immune response is also important from epidemiological point of view. To identify the co-infection scenario of HIV and HTLV-I with the CTLs effect we proposed in this paper a six compartmental ODE-model with uninfected, HIV-infected, HTLV-I infected CD4+T cells and free HIV virus particles with HIV specific CTLs and HTLV-I specific CTLs. The rate of infection of the cases are considered here saturated type and proliferation rate of uninfected and HIV infected CD4+ T-cells are of logistic terms. To establish the well-posedness of the model we have shown that the solution of the proposed model is non-negative and bounded. We obtain the basic reproduction number which is the maximum of the HIV-related reproduction and the HTLV-I related reproduction number. Along with the disease free equilibrium point the system contains other seven endemic equilibrium points containing infection by single disease or both. Analytically, we establish the local and global stability conditions of the equilibrium points and also we establish that the system experiences transcritical bifurcation by the generation of only HIV or HTLV-I infected endemic equilibrium point. Using numerical simulations, we validate the theoretical results and found two infection paths, one initiating with HIV and other with HTLV-I, both cases ultimately become co-infected. Finally, using the optimal control analysis we found the optimal policy for treatment using AVR, RTI & PI for HIV or AZT for HTLV-I control and lastly concluded by some recommendations.

Malicious Code Propagation Model Based on Sleep Monitoring Mechanism in Wireless Sensor Networks

&lt;p&gt;Wireless sensor networks (WSNs) are characterized by high node density and finite energy storage. Each node exchanges information with all its neighboring nodes frequently, which makes it easy for nodes to run out of energy, leading to paralysis of the WSNs when facing network malicious code attacks. To address this problem, a malicious code propagation model based on sleep-monitoring technology for WSNs is proposed. As a Multi-compartment propagation, sleep nodes and monitoring nodes are introduced to the conventional SIR model. Sleep nodes can turn the infected node into a dormant state and stop the dissemination of information to save energy. Monitoring nodes can contain malicious codes spread in wireless sensor networks by sharing prevention information in real time. Additionally, by calculating the equilibrium point and propagation threshold of the new feedback model, the corresponding Lyapunov function is constructed to prove the local stability and global stability of the equilibrium point. Finally, the results of numerical simulation experiments show that when the sleep rate is 0.3 and feedback rate is 0.0000005, the number of infected nodes in the wireless sensor network decreases by 43.45%. Therefore, adding sleep-monitoring technology can effectively control the spread of malicious code in the networks.&lt;/p&gt; &lt;p&gt;&amp;nbsp;&lt;/p&gt;

Analyzing Global Stability of M-Pox Disease Dynamics: Mathematical Insights into Detection and Treatment Strategies

In this research, a mathematical model is constructed to scrutinize the transmission patterns of monkeypox (mpox), with a specific emphasis on integrating the early detection of infected undetected individuals to curb its transmission. This research takes into account a range of factors influencing the propagation of monkeypox, encompassing population demographics, contact dynamics, and the efficacy of early detection of unidentified infected individuals. Employing the next-generation matrix method, the basic reproduction number (R0) is computed, revealing that the disease-free equilibrium state is locally asymptotically stable when (R0&lt;1). This suggests that containment of monkeypox is achievable within a human populace where (R0) remains below one (1), yet it transitions to an endemic state when (R0) exceeds this critical value one (1). Furthermore, a sensitivity analysis is conducted to evaluate the robustness of our findings to variations in model parameters. Utilizing numerical simulations conducted via MAPLE 18, we demonstrate the significance of prompt identification and immediate intervention for infected individuals who may otherwise go undetected, in effectively diminishing the dynamic propagation of monkeypox. The results underscore the pivotal role of early detection in mitigating monkeypox outbreaks and curtailing transmission rates.

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

In this paper, we derive the well-defined solutions to a θ-dimensional system of difference equations. We show that, the well-defined solutions to that system are represented in terms of Fibonacci and Lucas sequences. Moreover, we study the global stability of the solutions to that system. Finally, we give some numerical examples which confirm our theoretical results.

A Study of a Class Continuous SIR Epidemic Model with History

The SIR model, an epidemiological model, divides a population into three compartments: Susceptible (S), Infected (I), and Recovered (R). It is widely used to understand the spread of infectious diseases and predict epidemic outcomes based on factors such as transmission rates and population dynamics. A deterministic epidemic mathematical model to describe the transmission dynamics of an infectious disease was constructed and analyzed by incorporating memory term which provides information on the current and past disease states. The model revealed two key equilibria: a disease-free equilibrium and an endemic equilibrium. The calculated basic reproductive number R0, was employed to establish that when R0&lt;1, the disease-free equilibrium is locally asymptotically stable, while the endemic equilibrium is locally asymptotically stable when R0&gt;1. Additionally, we explored the global stability of these equilibria using Lyapunov functions and Dulac's method, respectively. To validate our analytical findings, we conducted numerical simulations of the model which show the importance of history in the dynamic spread and elimination of disease.

A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs

Today, the socio-cultural lack of some countries with increased urbanization has led to the unconscious breeding of stray dogs. The failure to care for the offspring of possessive dogs or ignoring the responsibility to find a suitable family for the offspring increased the dog population on the streets and in the shelters. In this study, our main target is to analyze the habitat of stray dogs and the strategy of how to control the population without damaging the ecosystem of the species. For this aim, we establish a fractional-order differential equation system to investigate the fractal dimension with long-term memory that invovles two compartments; the non-sterilized dog population (x(t)) and the sterilized one (y(t)). Firstly, we analyze the stability of the equilibrium points using the Routh-Hurwitz criteria to discuss cases that should not affect the ecosystem of the dog population, but control the stray dog population in the habitat. Since the intervention to the stray dog population occurs at discrete time impulses, we use the Euler method's discretization process to analyse the local and global stability around the equilibrium points. Besides this, we show that the solutions of the system represent semi-cycle behaviors. At the end of the study, we use accurate data to demonstrate the sterilization rate of stray dogs in their habitat.

Stability and co-existence state traveling wave solution for a general N-dimensional diffusive delayed Lotka-Volterra equation in a cylinder

Abstract A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+\infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.

A Mathematical Modeling of the Vaccination Effect on the SARS-CoV-2 Transmission: Analysis and Simulation

Several illustrative studies on the mathematical modeling and analysis of the Coronavirus have been carried out in a short period of time. There is not enough work that accounts for the vaccination campaign's two stages. In this work, a mathematical model is created to show the impact of the recent two-stage vaccination treatment on the Coronavirus. In the proposed model, five compartments are constructed, namely the susceptible individuals , the first dose of vaccination , the second dose of vaccination , infected and recovered population . The uniqueness, boundedness and existence of the solutions of this model have been discussed. All potential model equilibrium points are determined. The local as well as global stability of the system in terms of the basic reproduction number is investigated. Numerical simulation is also carried out to investigate the influence of parameters affecting the dynamics of the model and to support the gathered analytical findings of the model.

Fundamental Matrix, Integral Representation and Stability Analysis of the Solutions of Neutral Fractional Systems with Derivatives in the Riemann—Liouville Sense

The paper studies a class of nonlinear disturbed neutral linear fractional systems with derivatives in the the Riemann–Liouville sense and distributed delays. First, it is proved that the initial problem for these systems with discontinuous initial functions under some natural assumptions possesses a unique solution. The assumptions used for the proof are similar to those used in the case of systems with first-order derivatives. Then, with the obtained result, we derive the existence and uniqueness of a fundamental matrix and a generalized fundamental matrix for the homogeneous system. In the linear case, via these fundamental matrices we obtain integral representations of the solutions of the homogeneous system and the corresponding inhomogeneous system. Furthermore, for the fractional systems with Riemann–Liouville derivatives we introduce a new concept for weighted stabilities in the Lyapunov, Ulam–Hyers, and Ulam–Hyers–Rassias senses, which coincides with the classical stability concepts for the cases of integer-order or Caputo-type derivatives. It is proved that the zero solution of the homogeneous system is weighted stable if and only if all its solutions are weighted bounded. In addition, for the homogeneous system it is established that the weighted stability in the Lyapunov and Ulam–Hyers senses are equivalent if and only if the inequality appearing in the Ulam–Hyers definition possess only bounded solutions. Finally, we derive natural sufficient conditions under which the property of weighted global asymptotic stability of the zero solution of the homogeneous system is preserved under nonlinear disturbances.

Analysing the Impact of Influential Factors on Oil Prices: A Comprehensive Study

The interplay between macroeconomic indicators and oil prices has been a subject of intense scrutiny due to its far- reaching implications for global economic stability. This research paper undertakes a thorough investigation into the intricate relationship between various macroeconomic factors and the occurrence of oil price shocks. The study employs a multidimensional approach, encompassing both empirical analysis and theoretical frameworks, to elucidate the complex dynamics governing this interaction. The research begins by establishing a robust theoretical foundation, delving into existing economic models that elucidate the channels through which macroeconomic indicators influence oil prices. Recognising the intricate network of supply and demand forces, the paper explores the impact of key macroeconomic factors, including GDP growth, inflation rates, interest rates, and exchange rates, on the vulnerability of oil markets to price shocks. Methodologically, the research leverages advanced econometric techniques to analyse extensive datasets spanning multiple economies and time periods. A comprehensive panel data analysis is employed to capture the heterogeneity across different regions and economies, thereby providing a nuanced understanding of the global nature of the phenomenon. Additionally, time-series models are used to unravel the temporal dynamics of the relationship between macroeconomic indicators and oil price shocks. The findings of this research paper contribute significant insights to the existing body of knowledge. The empirical results shed light on the varying degrees of sensitivity that different macroeconomic indicators exhibit concerning oil price shocks. The study also uncovers potential feedback loops and non-linearities within the system, providing a more nuanced understanding of the relationship.

Analysis of the most probable exit path in the synthetic gene network with genetic toggle

In this paper, the most probable exit path is applied to understand the switching of a bistable synthetic gene network with genetic toggle in Escherichia coli from a new perspective. It is worth mentioning that the most probable exit path is a deterministic indicator for researching stochastic system, and its role is analogous to the phase diagram and time history diagram of deterministic system. Firstly, the large deviation theory proves that when a dynamic system has a stable equilibrium point, the cumulative effect of its long-term action can make its sample trajectory reach another region with a probability of 1 from the attractive region under weak random disturbance. The concept of the most probable exit path is given by defining Freidlin-Wentzell action functional. Moreover, considering the noise intensity, Onsager-Machlup action functional is defined to obtain the most probable exit path of the system subject to random disturbance. Based on the Onsager-Machlup action functional, it can be observed that the impact of two types of noise intensities on the most probable exit path for the transition of the system. In addition, based on vector field decomposition, energy landscape is used to analyze the global stability of the system. Finally, this article intuitively demonstrates the switching process of the system with genetic toggle. The analysis of Onsager-Machlup action functional reveals that two independent noises have opposite effects on the system switching. The increase in the intensity of the second Gaussian noise is conductive to more accurately observing the most probable exit path of the system. According to the energy landscape, the reduction of noise intensity is not conductive to switching of the system with genetic toggle.

What are developers talking about information security? A large-scale study using semantic analysis of Q&A posts.

Digitalization and rapid technological improvement in the present day bring numerous benefits, but they also raise the complexity and diversity of cyber security risks, putting critical information security issues on the agenda. Growing issues and worries about information security endanger not only the security of individuals and organizations but also global social and economic stability. This study investigates the issues and challenges regarding information security by analyzing all the postings on ISSE (Information Security Stack Exchange), a Q&A website focused on information security. In order to identify the primary topics addressed in postings shared on the ISSE platform, we employed a probabilistic topic modeling method called latent Dirichlet allocation (LDA), which is generative in nature and relies on unsupervised machine learning processes. Through this investigation, a total of 38 topics were identified, demonstrating the present state of information security issues and challenges. Considering these topics, a comprehensive taxonomy of seven categories was devised to address information security issues, taking into account their backgrounds and perspectives. Subsequently, we conducted an examination of the prevalence and complexity of the matters at hand. In addition, we have defined the prevailing technologies utilized in the realm of information security, including tasks, certifications, standards, methods, tools, threats, and defenses. We have provided a number of implications for different stakeholders, including academics, developers, educators, and practitioners, who are working towards advancing the field of information security.

Flatness-based control in successive loops for VSI-fed PM synchronous motors and induction motors

Electric traction systems consisting of inverter controlled three-phase motors are widely used in electric vehicles. In this article the control problem for the nonlinear dynamics of Voltage Source Inverter-fed synchronous and asynchronous motors is solved with the use of a flatness-based control approach which is implemented in successive loops. The state–space model of these systems is separated into a series of subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearised flat systems. In this chain of i = 1 , 2 , … , N subsystems, the state variables of the subsequent (i + 1th) subsystem become virtual control inputs for the preceding (ith) subsystem, and so on. In turn, exogenous control inputs are applied to the last subsystem and are computed by tracing backwards the virtual control inputs of the preceding N−1 subsystems. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The validity of the control method is confirmed in two case studies: (a) control of a Voltage Source Inverter-fed Permanent Magnet Synchronous Motor (VSI-fed PMSM), (ii) control of a Voltage Source Inverter-fed Induction Motor (VSI-fed IM).